---
_id: '15279'
abstract:
- lang: eng
  text: We formulate and prove an analog of Poonen’s finite-field Bertini theorem
    with Taylor conditions that holds in the Grothendieck ring of varieties. This
    gives a broad generalization of the work of Vakil and Wood, who treated the case
    of smooth hypersurface sections, and is made possible by the use of motivic Euler
    products to write down candidate motivic probabilities. As applications, we give
    motivic analogs of many results in arithmetic statistics that have been proven
    using Poonen’s sieve, including work of Bucur and Kedlaya on complete intersections
    and Erman and Wood on semiample Bertini theorems.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Margaret
  full_name: Bilu, Margaret
  id: 98C47862-10D5-11EA-BEDD-0F6F3DDC885E
  last_name: Bilu
- first_name: Sean
  full_name: Howe, Sean
  last_name: Howe
citation:
  ama: Bilu M, Howe S. Motivic Euler products in motivic statistics. <i>Algebra &#38;
    Number Theory</i>. 2021;15(9):2195-2259. doi:<a href="https://doi.org/10.2140/ant.2021.15.2195">10.2140/ant.2021.15.2195</a>
  apa: Bilu, M., &#38; Howe, S. (2021). Motivic Euler products in motivic statistics.
    <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/ant.2021.15.2195">https://doi.org/10.2140/ant.2021.15.2195</a>
  chicago: Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.”
    <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2021. <a
    href="https://doi.org/10.2140/ant.2021.15.2195">https://doi.org/10.2140/ant.2021.15.2195</a>.
  ieee: M. Bilu and S. Howe, “Motivic Euler products in motivic statistics,” <i>Algebra
    &#38; Number Theory</i>, vol. 15, no. 9. Mathematical Sciences Publishers, pp.
    2195–2259, 2021.
  ista: Bilu M, Howe S. 2021. Motivic Euler products in motivic statistics. Algebra
    &#38; Number Theory. 15(9), 2195–2259.
  mla: Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.”
    <i>Algebra &#38; Number Theory</i>, vol. 15, no. 9, Mathematical Sciences Publishers,
    2021, pp. 2195–259, doi:<a href="https://doi.org/10.2140/ant.2021.15.2195">10.2140/ant.2021.15.2195</a>.
  short: M. Bilu, S. Howe, Algebra &#38; Number Theory 15 (2021) 2195–2259.
corr_author: '1'
date_created: 2024-04-03T08:12:59Z
date_published: 2021-12-23T00:00:00Z
date_updated: 2024-10-21T06:02:15Z
day: '23'
department:
- _id: TiBr
doi: 10.2140/ant.2021.15.2195
external_id:
  arxiv:
  - '1910.05207'
intvolume: '        15'
issue: '9'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1910.05207
month: '12'
oa: 1
oa_version: Preprint
page: 2195-2259
publication: Algebra & Number Theory
publication_identifier:
  eissn:
  - 1944-7833
  issn:
  - 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Motivic Euler products in motivic statistics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2021'
...