A Lefschetz theorem for overconvergent isocrystals with Frobenius structure

Abe, Tomoyuki; Esnault, Hélène

doi:10.24033/asens.2408

A Lefschetz theorem for overconvergent isocrystals with Frobenius structure
[Un théorème de Leschetz pour les isocristaux surconvergents avec structure de Frobenius]

Abe, Tomoyuki ; Esnault, Hélène

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 5, pp. 1243-1264.

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Résumé
Abstract

Nous montrons un théorème de Lefschetz pour les $F$ -isocristaux surconvergents sur des variétés lisses définies sur un corps fini. Nous en tirons plusieurs conséquences.

We show a Lefschetz theorem for irreducible overconvergent $F$ -isocrystals on smooth varieties defined over a finite field. We derive several consequences from it.

Publié le : 2019-11-12

MR Zbl

DOI : 10.24033/asens.2408

Classification : 14F10, 14D20.
Keywords: Lefschetz theorem, overconvergent isocrystals, Frobenius structure.
Mot clés : Théorème de Leschetz, isocristaux surconvergents, structure de Frobenius.

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     author = {Abe, Tomoyuki and Esnault, H\'el\`ene},
     title = {A {Lefschetz} theorem for overconvergent isocrystals with {Frobenius} structure},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1243--1264},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 52},
     number = {5},
     year = {2019},
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     url = {http://www.numdam.org/articles/10.24033/asens.2408/}
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Abe, Tomoyuki; Esnault, Hélène. A Lefschetz theorem for overconvergent isocrystals with Frobenius structure. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 5, pp. 1243-1264. doi : 10.24033/asens.2408. http://www.numdam.org/articles/10.24033/asens.2408/

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