no. 5
Convergent isocrystals on simply connected varieties
[Isocristaux convergents sur des variétés simplement connexes]
Esnault, Hélène1 ; Shiho, Atsushi2
1 Freie Universität Berlin Arnimallee 3 14195 Berlin (Germany)
2 the University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba, Meguro-ku Tokyo 153-8914 (Japan)
Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2109-2148.

de Jong a conjecturé que sur une variété lisse projective connexe sur un corps algébriquement clos de caractéristique p>0, de groupe fondamental étale trivial, tout isocristal est constant. Nous prouvons cette conjecture sous certaines hypothèses supplémentaires.

It is conjectured by de Jong that, if X is a connected smooth projective variety over an algebraically closed field k of characteristic p>0 with trivial étale fundamental group, any isocrystal on X is constant. We prove this conjecture under certain additional assumptions.

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DOI : 10.5802/aif.3204
Classification : 14F10, 14D20
Keywords: isocrystals, simply connected varieties
Mot clés : isocristaux, variétés simplement connexes

Esnault, Hélène 1 ; Shiho, Atsushi 2

1 Freie Universität Berlin Arnimallee 3 14195 Berlin (Germany)
2 the University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba, Meguro-ku Tokyo 153-8914 (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Esnault, Hélène; Shiho, Atsushi. Convergent isocrystals on simply connected varieties. Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2109-2148. doi : 10.5802/aif.3204. https://aif.centre-mersenne.org/articles/10.5802/aif.3204/

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