---
_id: '60993'
abstract:
- lang: eng
  text: "<p>We determine the distribution of discriminants of wildly ramified elementary-abelian
    extensions of local and global function fields in characteristic <inline-formula
    content-type=\"math/mathml\">\r\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"
    alttext=\"p\">\r\n  <mml:semantics>\r\n    <mml:mi>p</mml:mi>\r\n    <mml:annotation
    encoding=\"application/x-tex\">p</mml:annotation>\r\n  </mml:semantics>\r\n</mml:math>\r\n</inline-formula>.
    For local and rational function fields, we also give precise formulae for the
    number of elementary-abelian extensions with a fixed discriminant divisor, which
    describe a local-global principle.</p>"
author:
- first_name: Nicolas
  full_name: Potthast, Nicolas
  id: '63958'
  last_name: Potthast
citation:
  ama: Potthast N. On the asymptotics of elementary-abelian extensions of local and
    global function fields. <i>Transactions of the American Mathematical Society</i>.
    2026;379(1):289-340. doi:<a href="https://doi.org/10.1090/tran/9509">10.1090/tran/9509</a>
  apa: Potthast, N. (2026). On the asymptotics of elementary-abelian extensions of
    local and global function fields. <i>Transactions of the American Mathematical
    Society</i>, <i>379</i>(1), 289–340. <a href="https://doi.org/10.1090/tran/9509">https://doi.org/10.1090/tran/9509</a>
  bibtex: '@article{Potthast_2026, title={On the asymptotics of elementary-abelian
    extensions of local and global function fields}, volume={379}, DOI={<a href="https://doi.org/10.1090/tran/9509">10.1090/tran/9509</a>},
    number={1}, journal={Transactions of the American Mathematical Society}, publisher={American
    Mathematical Society (AMS)}, author={Potthast, Nicolas}, year={2026}, pages={289–340}
    }'
  chicago: 'Potthast, Nicolas. “On the Asymptotics of Elementary-Abelian Extensions
    of Local and Global Function Fields.” <i>Transactions of the American Mathematical
    Society</i> 379, no. 1 (2026): 289–340. <a href="https://doi.org/10.1090/tran/9509">https://doi.org/10.1090/tran/9509</a>.'
  ieee: 'N. Potthast, “On the asymptotics of elementary-abelian extensions of local
    and global function fields,” <i>Transactions of the American Mathematical Society</i>,
    vol. 379, no. 1, pp. 289–340, 2026, doi: <a href="https://doi.org/10.1090/tran/9509">10.1090/tran/9509</a>.'
  mla: Potthast, Nicolas. “On the Asymptotics of Elementary-Abelian Extensions of
    Local and Global Function Fields.” <i>Transactions of the American Mathematical
    Society</i>, vol. 379, no. 1, American Mathematical Society (AMS), 2026, pp. 289–340,
    doi:<a href="https://doi.org/10.1090/tran/9509">10.1090/tran/9509</a>.
  short: N. Potthast, Transactions of the American Mathematical Society 379 (2026)
    289–340.
date_created: 2025-08-25T12:37:47Z
date_updated: 2025-12-12T08:40:53Z
doi: 10.1090/tran/9509
intvolume: '       379'
issue: '1'
language:
- iso: eng
page: 289 - 340
publication: Transactions of the American Mathematical Society
publication_identifier:
  issn:
  - 1088-6850
  - 0002-9947
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: On the asymptotics of elementary-abelian extensions of local and global function
  fields
type: journal_article
user_id: '63958'
volume: 379
year: '2026'
...