Convergent isocrystals on simply connected varieties

Esnault, Hélène; Shiho, Atsushi

doi:10.5802/aif.3204

Convergent isocrystals on simply connected varieties [ Isocristaux convergents sur des variétés simplement connexes ]

Esnault, Hélène ; Shiho, Atsushi

Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2109-2148.

Résumé
Abstract

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.

Reçu le : 2016-04-11
Révisé le : 2017-10-18
Accepté le : 2017-11-13
Publié le : 2018-11-22

DOI : https://doi.org/10.5802/aif.3204
Classification : 14F10, 14D20
Mots clés : isocristaux, variétés simplement connexes

@article{AIF_2018__68_5_2109_0,
     author = {Esnault, H\'el\`ene and Shiho, Atsushi},
     title = {Convergent isocrystals on simply connected varieties},
     journal = {Annales de l'Institut Fourier},
     pages = {2109--2148},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     doi = {10.5802/aif.3204},
     language = {en},
     url = {archive.numdam.org/item/AIF_2018__68_5_2109_0/}
}

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. http://archive.numdam.org/item/AIF_2018__68_5_2109_0/

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