---
_id: '64180'
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Gundlach F, Seguin BF. Asymptotics of extensions of simple ℚ-algebras. <i>Algebra
    &#38; Number Theory</i>. 2026;20(2):383-418. doi:<a href="https://doi.org/10.2140/ant.2026.20.383">10.2140/ant.2026.20.383</a>
  apa: Gundlach, F., &#38; Seguin, B. F. (2026). Asymptotics of extensions of simple
    ℚ-algebras. <i>Algebra &#38; Number Theory</i>, <i>20</i>(2), 383–418. <a href="https://doi.org/10.2140/ant.2026.20.383">https://doi.org/10.2140/ant.2026.20.383</a>
  bibtex: '@article{Gundlach_Seguin_2026, title={Asymptotics of extensions of simple
    ℚ-algebras}, volume={20}, DOI={<a href="https://doi.org/10.2140/ant.2026.20.383">10.2140/ant.2026.20.383</a>},
    number={2}, journal={Algebra &#38; Number Theory}, publisher={Mathematical Sciences
    Publishers}, author={Gundlach, Fabian and Seguin, Beranger Fabrice}, year={2026},
    pages={383–418} }'
  chicago: 'Gundlach, Fabian, and Beranger Fabrice Seguin. “Asymptotics of Extensions
    of Simple ℚ-Algebras.” <i>Algebra &#38; Number Theory</i> 20, no. 2 (2026): 383–418.
    <a href="https://doi.org/10.2140/ant.2026.20.383">https://doi.org/10.2140/ant.2026.20.383</a>.'
  ieee: 'F. Gundlach and B. F. Seguin, “Asymptotics of extensions of simple ℚ-algebras,”
    <i>Algebra &#38; Number Theory</i>, vol. 20, no. 2, pp. 383–418, 2026, doi: <a
    href="https://doi.org/10.2140/ant.2026.20.383">10.2140/ant.2026.20.383</a>.'
  mla: Gundlach, Fabian, and Beranger Fabrice Seguin. “Asymptotics of Extensions of
    Simple ℚ-Algebras.” <i>Algebra &#38; Number Theory</i>, vol. 20, no. 2, Mathematical
    Sciences Publishers, 2026, pp. 383–418, doi:<a href="https://doi.org/10.2140/ant.2026.20.383">10.2140/ant.2026.20.383</a>.
  short: F. Gundlach, B.F. Seguin, Algebra &#38; Number Theory 20 (2026) 383–418.
date_created: 2026-02-16T12:43:21Z
date_updated: 2026-02-17T13:02:21Z
doi: 10.2140/ant.2026.20.383
intvolume: '        20'
issue: '2'
language:
- iso: eng
page: 383-418
publication: Algebra & Number Theory
publication_identifier:
  issn:
  - 1944-7833
  - 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
status: public
title: Asymptotics of extensions of simple ℚ-algebras
type: journal_article
user_id: '102487'
volume: 20
year: '2026'
...
---
_id: '64913'
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
  orcid: 0000-0002-4800-4647
citation:
  ama: Gundlach F, Seguin BF. On matrices commuting with their Frobenius. <i>Journal
    of Algebra</i>. Published online 2026. doi:<a href="https://doi.org/10.1016/j.jalgebra.2026.02.025">10.1016/j.jalgebra.2026.02.025</a>
  apa: Gundlach, F., &#38; Seguin, B. F. (2026). On matrices commuting with their
    Frobenius. <i>Journal of Algebra</i>. <a href="https://doi.org/10.1016/j.jalgebra.2026.02.025">https://doi.org/10.1016/j.jalgebra.2026.02.025</a>
  bibtex: '@article{Gundlach_Seguin_2026, title={On matrices commuting with their
    Frobenius}, DOI={<a href="https://doi.org/10.1016/j.jalgebra.2026.02.025">10.1016/j.jalgebra.2026.02.025</a>},
    journal={Journal of Algebra}, publisher={Elsevier BV}, author={Gundlach, Fabian
    and Seguin, Beranger Fabrice}, year={2026} }'
  chicago: Gundlach, Fabian, and Beranger Fabrice Seguin. “On Matrices Commuting with
    Their Frobenius.” <i>Journal of Algebra</i>, 2026. <a href="https://doi.org/10.1016/j.jalgebra.2026.02.025">https://doi.org/10.1016/j.jalgebra.2026.02.025</a>.
  ieee: 'F. Gundlach and B. F. Seguin, “On matrices commuting with their Frobenius,”
    <i>Journal of Algebra</i>, 2026, doi: <a href="https://doi.org/10.1016/j.jalgebra.2026.02.025">10.1016/j.jalgebra.2026.02.025</a>.'
  mla: Gundlach, Fabian, and Beranger Fabrice Seguin. “On Matrices Commuting with
    Their Frobenius.” <i>Journal of Algebra</i>, Elsevier BV, 2026, doi:<a href="https://doi.org/10.1016/j.jalgebra.2026.02.025">10.1016/j.jalgebra.2026.02.025</a>.
  short: F. Gundlach, B.F. Seguin, Journal of Algebra (2026).
date_created: 2026-03-13T14:14:23Z
date_updated: 2026-03-13T14:15:17Z
doi: 10.1016/j.jalgebra.2026.02.025
language:
- iso: eng
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier BV
status: public
title: On matrices commuting with their Frobenius
type: journal_article
user_id: '100450'
year: '2026'
...
---
_id: '65031'
abstract:
- lang: eng
  text: We prove that two-step nilpotent $p$-extensions of rational global function
    fields of characteristic $p$ satisfy a quantitative local-global principle when
    they are counted according to their largest upper ramification break ("last jump").
    We had previously shown this only for $p\neq2$. Compared to our previous proof,
    this proof is also more self-contained, and may apply to heights other than the
    last jump. As an application, we describe the distribution of last jumps of $D_4$-extensions
    of rational global function fields of characteristic $2$. We also exhibit a counterexample
    to the analogous local-global principle when counting by discriminants.
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
  orcid: 0000-0002-4800-4647
citation:
  ama: Gundlach F, Seguin BF. Lifts of unramified twists and local-global principles.
    <i>arXiv:260315544</i>. Published online 2026.
  apa: Gundlach, F., &#38; Seguin, B. F. (2026). Lifts of unramified twists and local-global
    principles. In <i>arXiv:2603.15544</i>.
  bibtex: '@article{Gundlach_Seguin_2026, title={Lifts of unramified twists and local-global
    principles}, journal={arXiv:2603.15544}, author={Gundlach, Fabian and Seguin,
    Beranger Fabrice}, year={2026} }'
  chicago: Gundlach, Fabian, and Beranger Fabrice Seguin. “Lifts of Unramified Twists
    and Local-Global Principles.” <i>ArXiv:2603.15544</i>, 2026.
  ieee: F. Gundlach and B. F. Seguin, “Lifts of unramified twists and local-global
    principles,” <i>arXiv:2603.15544</i>. 2026.
  mla: Gundlach, Fabian, and Beranger Fabrice Seguin. “Lifts of Unramified Twists
    and Local-Global Principles.” <i>ArXiv:2603.15544</i>, 2026.
  short: F. Gundlach, B.F. Seguin, ArXiv:2603.15544 (2026).
date_created: 2026-03-17T12:17:42Z
date_updated: 2026-03-17T12:21:09Z
external_id:
  arxiv:
  - '2603.15544'
language:
- iso: eng
publication: arXiv:2603.15544
status: public
title: Lifts of unramified twists and local-global principles
type: preprint
user_id: '100450'
year: '2026'
...
---
_id: '58852'
abstract:
- lang: eng
  text: "We study the asymptotic distribution of wildly ramified extensions of\r\nfunction
    fields in characteristic $p > 2$, focusing on (certain) $p$-groups of\r\nnilpotency
    class at most $2$. Rather than the discriminant, we count extensions\r\naccording
    to an invariant describing the last jump in the ramification\r\nfiltration at
    each place. We prove a local-global principle relating the\r\ndistribution of
    extensions over global function fields to their distribution\r\nover local fields,
    leading to an asymptotic formula for the number of\r\nextensions with a given
    global last-jump invariant. A key ingredient is\r\nAbrashkin's nilpotent Artin-Schreier
    theory, which lets us parametrize\r\nextensions and obtain bounds on the ramification
    of local extensions by\r\nestimating the number of solutions to certain polynomial
    equations over finite\r\nfields."
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Gundlach F, Seguin BF. Counting two-step nilpotent wildly ramified extensions
    of function  fields. <i>arXiv:250218207</i>. Published online 2025.
  apa: Gundlach, F., &#38; Seguin, B. F. (2025). Counting two-step nilpotent wildly
    ramified extensions of function  fields. In <i>arXiv:2502.18207</i>.
  bibtex: '@article{Gundlach_Seguin_2025, title={Counting two-step nilpotent wildly
    ramified extensions of function  fields}, journal={arXiv:2502.18207}, author={Gundlach,
    Fabian and Seguin, Beranger Fabrice}, year={2025} }'
  chicago: Gundlach, Fabian, and Beranger Fabrice Seguin. “Counting Two-Step Nilpotent
    Wildly Ramified Extensions of Function  Fields.” <i>ArXiv:2502.18207</i>, 2025.
  ieee: F. Gundlach and B. F. Seguin, “Counting two-step nilpotent wildly ramified
    extensions of function  fields,” <i>arXiv:2502.18207</i>. 2025.
  mla: Gundlach, Fabian, and Beranger Fabrice Seguin. “Counting Two-Step Nilpotent
    Wildly Ramified Extensions of Function  Fields.” <i>ArXiv:2502.18207</i>, 2025.
  short: F. Gundlach, B.F. Seguin, ArXiv:2502.18207 (2025).
date_created: 2025-02-26T08:51:57Z
date_updated: 2025-02-26T08:53:08Z
external_id:
  arxiv:
  - '2502.18207'
language:
- iso: eng
publication: arXiv:2502.18207
status: public
title: Counting two-step nilpotent wildly ramified extensions of function  fields
type: preprint
user_id: '100450'
year: '2025'
...
---
_id: '58187'
abstract:
- lang: eng
  text: "Let $K$ be a field of characteristic $0$ and $k \\geq 2$ be an integer. We\r\nprove
    that every $K$-linear bijection $f : K[X] \\to K[X]$ strongly preserving\r\nthe
    set of $k$-free polynomials (or the set of polynomials with a $k$-fold root\r\nin
    $K$) is a constant multiple of a $K$-algebra automorphism of $K[X]$, i.e.,\r\nthere
    are elements $a, c \\in K^{\\times}$, $b \\in K$ such that $f(P)(X) = c P(a\r\nX
    + b)$. When $K$ is a number field or $K=\\mathbb{R}$, we prove that similar\r\nstatements
    hold when $f$ preserves the set of polynomials with a root in $K$."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. Symmetries of various sets of polynomials. <i>Beiträge zur Algebra
    und Geometrie</i>. Published online 2025. doi:<a href="https://doi.org/10.1007/s13366-025-00800-2">10.1007/s13366-025-00800-2</a>
  apa: Seguin, B. F. (2025). Symmetries of various sets of polynomials. <i>Beiträge
    Zur Algebra Und Geometrie</i>. <a href="https://doi.org/10.1007/s13366-025-00800-2">https://doi.org/10.1007/s13366-025-00800-2</a>
  bibtex: '@article{Seguin_2025, title={Symmetries of various sets of polynomials},
    DOI={<a href="https://doi.org/10.1007/s13366-025-00800-2">10.1007/s13366-025-00800-2</a>},
    journal={Beiträge zur Algebra und Geometrie}, author={Seguin, Beranger Fabrice},
    year={2025} }'
  chicago: Seguin, Beranger Fabrice. “Symmetries of Various Sets of Polynomials.”
    <i>Beiträge Zur Algebra Und Geometrie</i>, 2025. <a href="https://doi.org/10.1007/s13366-025-00800-2">https://doi.org/10.1007/s13366-025-00800-2</a>.
  ieee: 'B. F. Seguin, “Symmetries of various sets of polynomials,” <i>Beiträge zur
    Algebra und Geometrie</i>, 2025, doi: <a href="https://doi.org/10.1007/s13366-025-00800-2">10.1007/s13366-025-00800-2</a>.'
  mla: Seguin, Beranger Fabrice. “Symmetries of Various Sets of Polynomials.” <i>Beiträge
    Zur Algebra Und Geometrie</i>, 2025, doi:<a href="https://doi.org/10.1007/s13366-025-00800-2">10.1007/s13366-025-00800-2</a>.
  short: B.F. Seguin, Beiträge Zur Algebra Und Geometrie (2025).
date_created: 2025-01-15T11:25:18Z
date_updated: 2025-07-16T13:51:54Z
doi: 10.1007/s13366-025-00800-2
external_id:
  arxiv:
  - '2407.09118'
language:
- iso: eng
publication: Beiträge zur Algebra und Geometrie
status: public
title: Symmetries of various sets of polynomials
type: journal_article
user_id: '102487'
year: '2025'
...
---
_id: '63078'
abstract:
- lang: eng
  text: "For a finite group $G$, we describe the asymptotic growth of the number of\r\nconnected
    components of Hurwitz spaces of marked $G$-covers (of both the affine\r\nand projective
    lines) whose monodromy classes are constrained in a certain way,\r\nas the number
    of branch points grows to infinity. More precisely, we compute\r\nboth the exponent
    and (in many cases) the coefficient of the leading monomial\r\nin the count of
    components containing covers whose monodromy group is a given\r\nsubgroup of $G$.
    By the work of Ellenberg, Tran, Venkatesh and Westerland, this\r\nasymptotic behavior
    is related to the distribution of field extensions\r\nof~$\\mathbb{F}_q(T)$ with
    Galois group $G$."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. Counting Components of Hurwitz Spaces. <i>Israel Journal of Mathematics</i>.
    Published online 2025. doi:<a href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>
  apa: Seguin, B. F. (2025). Counting Components of Hurwitz Spaces. <i>Israel Journal
    of Mathematics</i>. <a href="https://doi.org/10.1007/s11856-025-2848-5">https://doi.org/10.1007/s11856-025-2848-5</a>
  bibtex: '@article{Seguin_2025, title={Counting Components of Hurwitz Spaces}, DOI={<a
    href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>},
    journal={Israel Journal of Mathematics}, publisher={Springer Science and Business
    Media LLC}, author={Seguin, Beranger Fabrice}, year={2025} }'
  chicago: Seguin, Beranger Fabrice. “Counting Components of Hurwitz Spaces.” <i>Israel
    Journal of Mathematics</i>, 2025. <a href="https://doi.org/10.1007/s11856-025-2848-5">https://doi.org/10.1007/s11856-025-2848-5</a>.
  ieee: 'B. F. Seguin, “Counting Components of Hurwitz Spaces,” <i>Israel Journal
    of Mathematics</i>, 2025, doi: <a href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>.'
  mla: Seguin, Beranger Fabrice. “Counting Components of Hurwitz Spaces.” <i>Israel
    Journal of Mathematics</i>, Springer Science and Business Media LLC, 2025, doi:<a
    href="https://doi.org/10.1007/s11856-025-2848-5">10.1007/s11856-025-2848-5</a>.
  short: B.F. Seguin, Israel Journal of Mathematics (2025).
date_created: 2025-12-12T23:09:07Z
date_updated: 2025-12-12T23:12:23Z
doi: 10.1007/s11856-025-2848-5
language:
- iso: eng
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
  - 1565-8511
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Counting Components of Hurwitz Spaces
type: journal_article
user_id: '102487'
year: '2025'
...
---
_id: '63077'
abstract:
- lang: eng
  text: We study $n$-flimsy spaces, which are the topological spaces that remain connected
    when removing fewer than $n$ points but become disconnected when removing exactly
    $n$ points. We show that no such space exists for $n \geq 3$, and that the compact
    $2$-flimsy spaces are precisely the dense and order-complete cyclically ordered
    sets equipped with their order topology. Furthermore, we examine variants of the
    definition obtained by replacing connectedness by path-connectedness, where paths
    are either parametrized by $[0,1]$ or by arbitrary compact linear continua.
author:
- first_name: Robin
  full_name: Khanfir, Robin
  last_name: Khanfir
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Khanfir R, Seguin BF. Flimsy Spaces. <i>arXiv:251117745</i>. Published online
    2025.
  apa: Khanfir, R., &#38; Seguin, B. F. (2025). Flimsy Spaces. In <i>arXiv:2511.17745</i>.
  bibtex: '@article{Khanfir_Seguin_2025, title={Flimsy Spaces}, journal={arXiv:2511.17745},
    author={Khanfir, Robin and Seguin, Beranger Fabrice}, year={2025} }'
  chicago: Khanfir, Robin, and Beranger Fabrice Seguin. “Flimsy Spaces.” <i>ArXiv:2511.17745</i>,
    2025.
  ieee: R. Khanfir and B. F. Seguin, “Flimsy Spaces,” <i>arXiv:2511.17745</i>. 2025.
  mla: Khanfir, Robin, and Beranger Fabrice Seguin. “Flimsy Spaces.” <i>ArXiv:2511.17745</i>,
    2025.
  short: R. Khanfir, B.F. Seguin, ArXiv:2511.17745 (2025).
date_created: 2025-12-12T23:07:55Z
date_updated: 2025-12-12T23:12:38Z
external_id:
  arxiv:
  - '2511.17745'
language:
- iso: eng
publication: arXiv:2511.17745
status: public
title: Flimsy Spaces
type: preprint
user_id: '102487'
year: '2025'
...
---
_id: '58183'
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: 'Seguin BF. Covers of ℙ<sup>1</sup> and their moduli: where arithmetic, geometry
    and combinatorics meet. In: <i>MFO–RIMS Tandem Workshop: Arithmetic Homotopy and
    Galois Theory</i>. Vol 20. Oberwolfach Reports. European Mathematical Society
    - EMS - Publishing House GmbH; 2024:2377-2488. doi:<a href="https://doi.org/10.4171/owr/2023/42">10.4171/owr/2023/42</a>'
  apa: 'Seguin, B. F. (2024). Covers of ℙ<sup>1</sup> and their moduli: where arithmetic,
    geometry and combinatorics meet. <i>MFO–RIMS Tandem Workshop: Arithmetic Homotopy
    and Galois Theory</i>, <i>20</i>(3), 2377–2488. <a href="https://doi.org/10.4171/owr/2023/42">https://doi.org/10.4171/owr/2023/42</a>'
  bibtex: '@inproceedings{Seguin_2024, series={Oberwolfach Reports}, title={Covers
    of ℙ<sup>1</sup> and their moduli: where arithmetic, geometry and combinatorics
    meet}, volume={20}, DOI={<a href="https://doi.org/10.4171/owr/2023/42">10.4171/owr/2023/42</a>},
    number={3}, booktitle={MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois
    Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH},
    author={Seguin, Beranger Fabrice}, year={2024}, pages={2377–2488}, collection={Oberwolfach
    Reports} }'
  chicago: 'Seguin, Beranger Fabrice. “Covers of ℙ<sup>1</sup> and Their Moduli: Where
    Arithmetic, Geometry and Combinatorics Meet.” In <i>MFO–RIMS Tandem Workshop:
    Arithmetic Homotopy and Galois Theory</i>, 20:2377–2488. Oberwolfach Reports.
    European Mathematical Society - EMS - Publishing House GmbH, 2024. <a href="https://doi.org/10.4171/owr/2023/42">https://doi.org/10.4171/owr/2023/42</a>.'
  ieee: 'B. F. Seguin, “Covers of ℙ<sup>1</sup> and their moduli: where arithmetic,
    geometry and combinatorics meet,” in <i>MFO–RIMS Tandem Workshop: Arithmetic Homotopy
    and Galois Theory</i>, 2024, vol. 20, no. 3, pp. 2377–2488, doi: <a href="https://doi.org/10.4171/owr/2023/42">10.4171/owr/2023/42</a>.'
  mla: 'Seguin, Beranger Fabrice. “Covers of ℙ<sup>1</sup> and Their Moduli: Where
    Arithmetic, Geometry and Combinatorics Meet.” <i>MFO–RIMS Tandem Workshop: Arithmetic
    Homotopy and Galois Theory</i>, vol. 20, no. 3, European Mathematical Society
    - EMS - Publishing House GmbH, 2024, pp. 2377–488, doi:<a href="https://doi.org/10.4171/owr/2023/42">10.4171/owr/2023/42</a>.'
  short: 'B.F. Seguin, in: MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois
    Theory, European Mathematical Society - EMS - Publishing House GmbH, 2024, pp.
    2377–2488.'
date_created: 2025-01-15T10:59:41Z
date_updated: 2025-01-15T11:28:57Z
doi: 10.4171/owr/2023/42
intvolume: '        20'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://beranger-seguin.fr/assets/pdf/abstract_mfo.pdf
page: 2377-2488
publication: 'MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory'
publication_identifier:
  issn:
  - 1660-8933
  - 1660-8941
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
series_title: Oberwolfach Reports
status: public
title: 'Covers of ℙ¹ and their moduli: where arithmetic, geometry and combinatorics
  meet'
type: conference_abstract
user_id: '102487'
volume: 20
year: '2024'
...
---
_id: '58182'
abstract:
- lang: eng
  text: 'We study a weak divisibility property for noncommutative rings: a nontrivial
    ring is fadelian if for all nonzero a and x there exist b, c such that x=ab+ca.
    We prove properties of fadelian rings and construct examples thereof which are
    not division rings, as well as non-Noetherian and non-Ore examples.'
author:
- first_name: Robin
  full_name: Khanfir, Robin
  last_name: Khanfir
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Khanfir R, Seguin BF. Study of a division-like property. <i>Journal of Algebra
    and Its Applications</i>. Published online 2024. doi:<a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>
  apa: Khanfir, R., &#38; Seguin, B. F. (2024). Study of a division-like property.
    <i>Journal of Algebra and Its Applications</i>. <a href="https://doi.org/10.1142/s0219498825502214">https://doi.org/10.1142/s0219498825502214</a>
  bibtex: '@article{Khanfir_Seguin_2024, title={Study of a division-like property},
    DOI={<a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>},
    journal={Journal of Algebra and Its Applications}, publisher={World Scientific
    Pub Co Pte Ltd}, author={Khanfir, Robin and Seguin, Beranger Fabrice}, year={2024}
    }'
  chicago: Khanfir, Robin, and Beranger Fabrice Seguin. “Study of a Division-like
    Property.” <i>Journal of Algebra and Its Applications</i>, 2024. <a href="https://doi.org/10.1142/s0219498825502214">https://doi.org/10.1142/s0219498825502214</a>.
  ieee: 'R. Khanfir and B. F. Seguin, “Study of a division-like property,” <i>Journal
    of Algebra and Its Applications</i>, 2024, doi: <a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>.'
  mla: Khanfir, Robin, and Beranger Fabrice Seguin. “Study of a Division-like Property.”
    <i>Journal of Algebra and Its Applications</i>, World Scientific Pub Co Pte Ltd,
    2024, doi:<a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>.
  short: R. Khanfir, B.F. Seguin, Journal of Algebra and Its Applications (2024).
date_created: 2025-01-15T10:59:30Z
date_updated: 2025-01-15T11:35:29Z
doi: 10.1142/s0219498825502214
language:
- iso: eng
main_file_link:
- url: https://beranger-seguin.fr/dmi/fadelian/fadrings.pdf
publication: Journal of Algebra and Its Applications
publication_identifier:
  issn:
  - 0219-4988
  - 1793-6829
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Study of a division-like property
type: journal_article
user_id: '102487'
year: '2024'
...
---
_id: '58189'
abstract:
- lang: eng
  text: "Hurwitz spaces are moduli spaces that classify ramified covers of the projective
    line on\r\nwhich a fixed group G acts. Their geometric and arithmetic properties
    are related to\r\nnumber theoretical questions, particularly the inverse Galois
    problem. In this thesis, we\r\nstudy the connected components of these spaces.
    Firstly, we prove results concerning\r\nthe asymptotic behavior of the count of
    connected components of Hurwitz spaces as\r\nthe number of branch points of the
    covers they classify grows. Secondly, we establish\r\nstability results for fields
    of definitions of connected components of Hurwitz spaces\r\nunder the gluing operation.
    These results relate topological and arithmetical properties\r\nof covers. Three
    expository chapters, devoid of original statements, present the various\r\nobjects.
    In an appendix, we summarize the thesis for the general public."
- lang: fre
  text: "Les espaces de Hurwitz sont des espaces de modules qui classifient les revêtements\r\nramifiés
    de la droite projective sur lesquels un groupe G, fixé, agit. Leurs propriétés\r\ngéométriques
    et arithmétiques sont liées à des questions de théorie des nombres, et no-\r\ntamment
    au problème de Galois inverse. Dans cette thèse, on étudie les composantes\r\nconnexes
    de ces espaces. Dans un premier temps, on démontre des résultats concer-\r\nnant
    l’évolution du nombre de composantes connexes des espaces de Hurwitz à mesure\r\nque
    le nombre de points de branchement des revêtements qu’ils classifient augmente.\r\nDans
    un second temps, on démontre des résultats de stabilité, sous l’opération de rec-\r\nollement
    des composantes connexes des espaces de Hurwitz, de leur corps de défini-\r\ntion.
    Ces résultats relient les propriétés topologiques et arithmétiques des revêtements.\r\nTrois
    chapitres d’exposition, dénués d’énoncés originaux, présentent les différents
    ob-\r\njets étudiés. Dans un appendice, on résume la thèse à l’attention du grand
    public."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. <i>Geometry and Arithmetic of Components of Hurwitz Spaces</i>.;
    2023.
  apa: Seguin, B. F. (2023). <i>Geometry and arithmetic of components of Hurwitz spaces</i>.
  bibtex: '@book{Seguin_2023, title={Geometry and arithmetic of components of Hurwitz
    spaces}, author={Seguin, Beranger Fabrice}, year={2023} }'
  chicago: Seguin, Beranger Fabrice. <i>Geometry and Arithmetic of Components of Hurwitz
    Spaces</i>, 2023.
  ieee: B. F. Seguin, <i>Geometry and arithmetic of components of Hurwitz spaces</i>.
    2023.
  mla: Seguin, Beranger Fabrice. <i>Geometry and Arithmetic of Components of Hurwitz
    Spaces</i>. 2023.
  short: B.F. Seguin, Geometry and Arithmetic of Components of Hurwitz Spaces, 2023.
date_created: 2025-01-15T11:27:06Z
date_updated: 2025-01-15T11:29:06Z
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://beranger-seguin.fr/these.pdf
status: public
title: Geometry and arithmetic of components of Hurwitz spaces
type: dissertation
user_id: '102487'
year: '2023'
...
---
_id: '58184'
abstract:
- lang: eng
  text: "For a fixed finite group $G$, we study the fields of definition of\r\ngeometrically
    irreducible components of Hurwitz moduli schemes of marked\r\nbranched $G$-covers
    of the projective line. The main focus is on determining\r\nwhether components
    obtained by \"gluing\" two other components, both defined over\r\na number field
    $K$, are also defined over $K$. The article presents a list of\r\nsituations in
    which a positive answer is obtained. As an application, when $G$\r\nis a semi-direct
    product of symmetric groups or the Mathieu group $M_{23}$,\r\ncomponents defined
    over $\\mathbb{Q}$ of small dimension ($6$ and $4$,\r\nrespectively) are shown
    to exist."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. Fields of Definition of Components of Hurwitz Spaces. <i>arXiv:230305903</i>.
    Published online 2023.
  apa: Seguin, B. F. (2023). Fields of Definition of Components of Hurwitz Spaces.
    In <i>arXiv:2303.05903</i>.
  bibtex: '@article{Seguin_2023, title={Fields of Definition of Components of Hurwitz
    Spaces}, journal={arXiv:2303.05903}, author={Seguin, Beranger Fabrice}, year={2023}
    }'
  chicago: Seguin, Beranger Fabrice. “Fields of Definition of Components of Hurwitz
    Spaces.” <i>ArXiv:2303.05903</i>, 2023.
  ieee: B. F. Seguin, “Fields of Definition of Components of Hurwitz Spaces,” <i>arXiv:2303.05903</i>.
    2023.
  mla: Seguin, Beranger Fabrice. “Fields of Definition of Components of Hurwitz Spaces.”
    <i>ArXiv:2303.05903</i>, 2023.
  short: B.F. Seguin, ArXiv:2303.05903 (2023).
date_created: 2025-01-15T11:24:23Z
date_updated: 2025-01-15T11:35:23Z
external_id:
  arxiv:
  - '2303.05903'
language:
- iso: eng
publication: arXiv:2303.05903
status: public
title: Fields of Definition of Components of Hurwitz Spaces
type: preprint
user_id: '102487'
year: '2023'
...
---
_id: '58185'
abstract:
- lang: eng
  text: "We consider a variant of the ring of components of Hurwitz spaces introduced\r\nby
    Ellenberg, Venkatesh and Westerland. By focusing on Hurwitz spaces\r\nclassifying
    covers of the projective line, the resulting ring of components is\r\ncommutative,
    which lets us study it from the point of view of algebraic\r\ngeometry and relate
    its geometric properties to numerical invariants involved\r\nin our previously
    obtained asymptotic counts. Specifically, we describe a\r\nstratification of the
    prime spectrum of the ring of components, and we compute\r\nthe dimensions and
    degrees of the strata. Using the stratification, we give a\r\ncomplete description
    of the spectrum in some cases."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. The Geometry of Rings of Components of Hurwitz Spaces. <i>arXiv:221012793</i>.
    Published online 2022.
  apa: Seguin, B. F. (2022). The Geometry of Rings of Components of Hurwitz Spaces.
    In <i>arXiv:2210.12793</i>.
  bibtex: '@article{Seguin_2022, title={The Geometry of Rings of Components of Hurwitz
    Spaces}, journal={arXiv:2210.12793}, author={Seguin, Beranger Fabrice}, year={2022}
    }'
  chicago: Seguin, Beranger Fabrice. “The Geometry of Rings of Components of Hurwitz
    Spaces.” <i>ArXiv:2210.12793</i>, 2022.
  ieee: B. F. Seguin, “The Geometry of Rings of Components of Hurwitz Spaces,” <i>arXiv:2210.12793</i>.
    2022.
  mla: Seguin, Beranger Fabrice. “The Geometry of Rings of Components of Hurwitz Spaces.”
    <i>ArXiv:2210.12793</i>, 2022.
  short: B.F. Seguin, ArXiv:2210.12793 (2022).
date_created: 2025-01-15T11:24:56Z
date_updated: 2025-01-15T11:35:43Z
external_id:
  arxiv:
  - '2210.12793'
language:
- iso: eng
publication: arXiv:2210.12793
status: public
title: The Geometry of Rings of Components of Hurwitz Spaces
type: preprint
user_id: '102487'
year: '2022'
...
---
_id: '58190'
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. <i>Les Déformations des Représentations Galoisiennes</i>.
  apa: Seguin, B. F. (n.d.). <i>Les Déformations des Représentations Galoisiennes</i>.
  bibtex: '@book{Seguin, title={Les Déformations des Représentations Galoisiennes},
    author={Seguin, Beranger Fabrice} }'
  chicago: Seguin, Beranger Fabrice. <i>Les Déformations des Représentations Galoisiennes</i>,
    n.d.
  ieee: B. F. Seguin, <i>Les Déformations des Représentations Galoisiennes</i>. .
  mla: Seguin, Beranger Fabrice. <i>Les Déformations des Représentations Galoisiennes</i>.
  short: B.F. Seguin, Les Déformations des Représentations Galoisiennes, n.d.
date_created: 2025-01-15T11:34:54Z
date_updated: 2025-01-15T11:34:59Z
extern: '1'
language:
- iso: fre
main_file_link:
- url: https://beranger-seguin.fr/assets/pdf/memoire.pdf
publication_status: unpublished
status: public
title: Les Déformations des Représentations Galoisiennes
type: mastersthesis
user_id: '102487'
year: '2019'
...