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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Bertini irreducibility theorems over finite fields
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by François Charles and Bjorn Poonen
J. Amer. Math. Soc. 29 (2016), 81-94
DOI: https://doi.org/10.1090/S0894-0347-2014-00820-1
Published electronically: October 31, 2014

Erratum: J. Amer. Math. Soc. 32 (2019), 605-607.

Abstract:

Given a geometrically irreducible subscheme $X \subseteq \mathbb {P}^n_{\mathbb {F}_q}$ of dimension at least $2$, we prove that the fraction of degree $d$ hypersurfaces $H$ such that $H \cap X$ is geometrically irreducible tends to $1$ as $d \to \infty$. We also prove variants in which $X$ is over an extension of $\mathbb {F}_q$, and in which the immersion $X \to \mathbb {P}^n_{\mathbb {F}_q}$ is replaced by a more general morphism.
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Bibliographic Information
  • François Charles
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307; and CNRS, Laboratoire de Mathématiques d’Orsay,Université Paris-Sud, 91405 Orsay CEDEX, France
  • Email: francois.charles@math.u-psud.fr
  • Bjorn Poonen
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
  • MR Author ID: 250625
  • ORCID: 0000-0002-8593-2792
  • Email: poonen@math.mit.edu
  • Received by editor(s): November 27, 2013
  • Received by editor(s) in revised form: July 4, 2014, July 7, 2014, and September 15, 2014
  • Published electronically: October 31, 2014
  • Additional Notes: This material is based upon work supported by the National Science Foundation under grant number DMS-1069236. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 29 (2016), 81-94
  • MSC (2010): Primary 14J70; Secondary 14N05
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00820-1
  • MathSciNet review: 3402695