[{"user_id":"102487","_id":"64180","language":[{"iso":"eng"}],"publication":"Algebra & Number Theory","type":"journal_article","status":"public","volume":20,"date_created":"2026-02-16T12:43:21Z","author":[{"last_name":"Gundlach","full_name":"Gundlach, Fabian","id":"100450","first_name":"Fabian"},{"full_name":"Seguin, Beranger Fabrice","id":"102487","last_name":"Seguin","first_name":"Beranger Fabrice"}],"publisher":"Mathematical Sciences Publishers","date_updated":"2026-02-17T13:02:21Z","doi":"10.2140/ant.2026.20.383","title":"Asymptotics of extensions of simple ℚ-algebras","issue":"2","publication_identifier":{"issn":["1944-7833","1937-0652"]},"publication_status":"published","intvolume":"        20","page":"383-418","citation":{"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>","short":"F. Gundlach, B.F. Seguin, Algebra &#38; Number Theory 20 (2026) 383–418.","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>.","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} }","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>.","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>.","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>"},"year":"2026"},{"citation":{"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>.","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>.","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} }","short":"F. Gundlach, B.F. Seguin, Journal of Algebra (2026).","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>."},"year":"2026","publication_identifier":{"issn":["0021-8693"]},"publication_status":"published","doi":"10.1016/j.jalgebra.2026.02.025","title":"On matrices commuting with their Frobenius","date_created":"2026-03-13T14:14:23Z","author":[{"id":"100450","full_name":"Gundlach, Fabian","last_name":"Gundlach","first_name":"Fabian"},{"first_name":"Beranger Fabrice","id":"102487","full_name":"Seguin, Beranger Fabrice","last_name":"Seguin","orcid":"0000-0002-4800-4647"}],"date_updated":"2026-03-13T14:15:17Z","publisher":"Elsevier BV","status":"public","publication":"Journal of Algebra","type":"journal_article","language":[{"iso":"eng"}],"user_id":"100450","_id":"64913"},{"citation":{"apa":"Gundlach, F., &#38; Seguin, B. F. (2026). Lifts of unramified twists and local-global principles. In <i>arXiv:2603.15544</i>.","ama":"Gundlach F, Seguin BF. Lifts of unramified twists and local-global principles. <i>arXiv:260315544</i>. Published online 2026.","short":"F. Gundlach, B.F. Seguin, ArXiv:2603.15544 (2026).","mla":"Gundlach, Fabian, and Beranger Fabrice Seguin. “Lifts of Unramified Twists and Local-Global Principles.” <i>ArXiv:2603.15544</i>, 2026.","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."},"year":"2026","date_created":"2026-03-17T12:17:42Z","author":[{"full_name":"Gundlach, Fabian","id":"100450","last_name":"Gundlach","first_name":"Fabian"},{"last_name":"Seguin","orcid":"0000-0002-4800-4647","full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice"}],"date_updated":"2026-03-17T12:21:09Z","title":"Lifts of unramified twists and local-global principles","type":"preprint","publication":"arXiv:2603.15544","status":"public","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."}],"user_id":"100450","_id":"65031","external_id":{"arxiv":["2603.15544"]},"language":[{"iso":"eng"}]},{"year":"2025","citation":{"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} }","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).","ieee":"F. Gundlach and B. F. Seguin, “Counting two-step nilpotent wildly ramified extensions of function  fields,” <i>arXiv:2502.18207</i>. 2025.","chicago":"Gundlach, Fabian, and Beranger Fabrice Seguin. “Counting Two-Step Nilpotent Wildly Ramified Extensions of Function  Fields.” <i>ArXiv:2502.18207</i>, 2025.","ama":"Gundlach F, Seguin BF. Counting two-step nilpotent wildly ramified extensions of function  fields. <i>arXiv:250218207</i>. Published online 2025."},"date_updated":"2025-02-26T08:53:08Z","author":[{"last_name":"Gundlach","full_name":"Gundlach, Fabian","id":"100450","first_name":"Fabian"},{"last_name":"Seguin","id":"102487","full_name":"Seguin, Beranger Fabrice","first_name":"Beranger Fabrice"}],"date_created":"2025-02-26T08:51:57Z","title":"Counting two-step nilpotent wildly ramified extensions of function  fields","type":"preprint","publication":"arXiv:2502.18207","abstract":[{"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.","lang":"eng"}],"status":"public","external_id":{"arxiv":["2502.18207"]},"_id":"58852","user_id":"100450","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"user_id":"102487","_id":"58187","external_id":{"arxiv":["2407.09118"]},"status":"public","abstract":[{"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 $K$.","lang":"eng"}],"publication":"Beiträge zur Algebra und Geometrie","type":"journal_article","doi":"10.1007/s13366-025-00800-2","title":"Symmetries of various sets of polynomials","date_created":"2025-01-15T11:25:18Z","author":[{"last_name":"Seguin","id":"102487","full_name":"Seguin, Beranger Fabrice","first_name":"Beranger Fabrice"}],"date_updated":"2025-07-16T13:51:54Z","citation":{"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>.","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>.","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>","short":"B.F. Seguin, Beiträge Zur Algebra Und Geometrie (2025).","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>.","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} }","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>"},"year":"2025"},{"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 $G$."}],"status":"public","publication":"Israel Journal of Mathematics","type":"journal_article","language":[{"iso":"eng"}],"_id":"63078","user_id":"102487","year":"2025","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>","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>.","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>","short":"B.F. Seguin, Israel Journal of Mathematics (2025).","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} }","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>."},"publication_identifier":{"issn":["0021-2172","1565-8511"]},"publication_status":"published","title":"Counting Components of Hurwitz Spaces","doi":"10.1007/s11856-025-2848-5","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-12T23:12:23Z","author":[{"last_name":"Seguin","full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice"}],"date_created":"2025-12-12T23:09:07Z"},{"publication":"arXiv:2511.17745","type":"preprint","status":"public","abstract":[{"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.","lang":"eng"}],"user_id":"102487","external_id":{"arxiv":["2511.17745"]},"_id":"63077","language":[{"iso":"eng"}],"citation":{"ieee":"R. Khanfir and B. F. Seguin, “Flimsy Spaces,” <i>arXiv:2511.17745</i>. 2025.","chicago":"Khanfir, Robin, and Beranger Fabrice Seguin. “Flimsy Spaces.” <i>ArXiv:2511.17745</i>, 2025.","ama":"Khanfir R, Seguin BF. Flimsy Spaces. <i>arXiv:251117745</i>. Published online 2025.","bibtex":"@article{Khanfir_Seguin_2025, title={Flimsy Spaces}, journal={arXiv:2511.17745}, author={Khanfir, Robin and Seguin, Beranger Fabrice}, year={2025} }","short":"R. Khanfir, B.F. Seguin, ArXiv:2511.17745 (2025).","mla":"Khanfir, Robin, and Beranger Fabrice Seguin. “Flimsy Spaces.” <i>ArXiv:2511.17745</i>, 2025.","apa":"Khanfir, R., &#38; Seguin, B. F. (2025). Flimsy Spaces. In <i>arXiv:2511.17745</i>."},"year":"2025","date_created":"2025-12-12T23:07:55Z","author":[{"first_name":"Robin","full_name":"Khanfir, Robin","last_name":"Khanfir"},{"first_name":"Beranger Fabrice","id":"102487","full_name":"Seguin, Beranger Fabrice","last_name":"Seguin"}],"date_updated":"2025-12-12T23:12:38Z","title":"Flimsy Spaces"},{"language":[{"iso":"eng"}],"user_id":"102487","series_title":"Oberwolfach Reports","_id":"58183","status":"public","type":"conference_abstract","publication":"MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory","main_file_link":[{"url":"https://beranger-seguin.fr/assets/pdf/abstract_mfo.pdf"}],"doi":"10.4171/owr/2023/42","title":"Covers of ℙ¹ and their moduli: where arithmetic, geometry and combinatorics meet","date_created":"2025-01-15T10:59:41Z","author":[{"last_name":"Seguin","full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice"}],"volume":20,"date_updated":"2025-01-15T11:28:57Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH","citation":{"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>.","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>","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} }","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.","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>"},"intvolume":"        20","page":"2377-2488","year":"2024","issue":"3","publication_status":"published","publication_identifier":{"issn":["1660-8933","1660-8941"]}},{"title":"Study of a division-like property","doi":"10.1142/s0219498825502214","main_file_link":[{"url":"https://beranger-seguin.fr/dmi/fadelian/fadrings.pdf"}],"date_updated":"2025-01-15T11:35:29Z","publisher":"World Scientific Pub Co Pte Ltd","date_created":"2025-01-15T10:59:30Z","author":[{"first_name":"Robin","full_name":"Khanfir, Robin","last_name":"Khanfir"},{"first_name":"Beranger Fabrice","id":"102487","full_name":"Seguin, Beranger Fabrice","last_name":"Seguin"}],"year":"2024","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>","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>.","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} }","short":"R. Khanfir, B.F. Seguin, Journal of Algebra and Its Applications (2024).","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>."},"publication_identifier":{"issn":["0219-4988","1793-6829"]},"publication_status":"published","language":[{"iso":"eng"}],"_id":"58182","user_id":"102487","abstract":[{"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.","lang":"eng"}],"status":"public","publication":"Journal of Algebra and Its Applications","type":"journal_article"},{"type":"dissertation","status":"public","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."},{"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.","lang":"fre"}],"user_id":"102487","_id":"58189","language":[{"iso":"eng"}],"extern":"1","citation":{"ama":"Seguin BF. <i>Geometry and Arithmetic of Components of Hurwitz Spaces</i>.; 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.","bibtex":"@book{Seguin_2023, title={Geometry and arithmetic of components of Hurwitz spaces}, author={Seguin, Beranger Fabrice}, year={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.","apa":"Seguin, B. F. (2023). <i>Geometry and arithmetic of components of Hurwitz spaces</i>."},"year":"2023","author":[{"last_name":"Seguin","full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice"}],"date_created":"2025-01-15T11:27:06Z","date_updated":"2025-01-15T11:29:06Z","main_file_link":[{"url":"https://beranger-seguin.fr/these.pdf"}],"title":"Geometry and arithmetic of components of Hurwitz spaces"},{"year":"2023","citation":{"ama":"Seguin BF. Fields of Definition of Components of Hurwitz Spaces. <i>arXiv:230305903</i>. Published online 2023.","ieee":"B. F. Seguin, “Fields of Definition of Components of Hurwitz Spaces,” <i>arXiv:2303.05903</i>. 2023.","chicago":"Seguin, Beranger Fabrice. “Fields of Definition of Components of Hurwitz Spaces.” <i>ArXiv:2303.05903</i>, 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} }","short":"B.F. Seguin, ArXiv:2303.05903 (2023).","mla":"Seguin, Beranger Fabrice. “Fields of Definition of Components of Hurwitz Spaces.” <i>ArXiv:2303.05903</i>, 2023."},"date_updated":"2025-01-15T11:35:23Z","date_created":"2025-01-15T11:24:23Z","author":[{"id":"102487","full_name":"Seguin, Beranger Fabrice","last_name":"Seguin","first_name":"Beranger Fabrice"}],"title":"Fields of Definition of Components of Hurwitz Spaces","publication":"arXiv:2303.05903","type":"preprint","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."}],"status":"public","external_id":{"arxiv":["2303.05903"]},"_id":"58184","user_id":"102487","language":[{"iso":"eng"}]},{"publication":"arXiv:2210.12793","type":"preprint","abstract":[{"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.","lang":"eng"}],"status":"public","_id":"58185","external_id":{"arxiv":["2210.12793"]},"user_id":"102487","language":[{"iso":"eng"}],"year":"2022","citation":{"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} }","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).","ieee":"B. F. Seguin, “The Geometry of Rings of Components of Hurwitz Spaces,” <i>arXiv:2210.12793</i>. 2022.","chicago":"Seguin, Beranger Fabrice. “The Geometry of Rings of Components of Hurwitz Spaces.” <i>ArXiv:2210.12793</i>, 2022.","ama":"Seguin BF. The Geometry of Rings of Components of Hurwitz Spaces. <i>arXiv:221012793</i>. Published online 2022."},"date_updated":"2025-01-15T11:35:43Z","date_created":"2025-01-15T11:24:56Z","author":[{"last_name":"Seguin","full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice"}],"title":"The Geometry of Rings of Components of Hurwitz Spaces"},{"status":"public","type":"mastersthesis","extern":"1","language":[{"iso":"fre"}],"user_id":"102487","_id":"58190","citation":{"ieee":"B. F. Seguin, <i>Les Déformations des Représentations Galoisiennes</i>. .","chicago":"Seguin, Beranger Fabrice. <i>Les Déformations des Représentations Galoisiennes</i>, n.d.","ama":"Seguin BF. <i>Les Déformations des Représentations Galoisiennes</i>.","short":"B.F. Seguin, Les Déformations des Représentations Galoisiennes, n.d.","bibtex":"@book{Seguin, title={Les Déformations des Représentations Galoisiennes}, author={Seguin, Beranger Fabrice} }","mla":"Seguin, Beranger Fabrice. <i>Les Déformations des Représentations Galoisiennes</i>.","apa":"Seguin, B. F. (n.d.). <i>Les Déformations des Représentations Galoisiennes</i>."},"year":"2019","publication_status":"unpublished","main_file_link":[{"url":"https://beranger-seguin.fr/assets/pdf/memoire.pdf"}],"title":"Les Déformations des Représentations Galoisiennes","date_created":"2025-01-15T11:34:54Z","author":[{"first_name":"Beranger Fabrice","id":"102487","full_name":"Seguin, Beranger Fabrice","last_name":"Seguin"}],"date_updated":"2025-01-15T11:34:59Z"}]