Geodesic
Bertini irreducibility theorems over finite fields
Charles, François1 ; Poonen, Bjorn2
1 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
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
Journal of the American Mathematical Society, Tome 29 (2016) no. 1, pp. 81-94

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-2014-00820-1

Charles, François 1 ; Poonen, Bjorn 2

1 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
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 
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Charles, François; Poonen, Bjorn. Bertini irreducibility theorems over finite fields. Journal of the American Mathematical Society, Tome 29 (2016) no. 1, pp. 81-94. doi: 10.1090/S0894-0347-2014-00820-1

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