Convergent isocrystals on simply connected varieties

Esnault, Hélène; Shiho, Atsushi

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

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.

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.

Classification: 14F10, 14D20
Keywords: isocrystals, simply connected varieties
Mot clés : isocristaux, variétés simplement connexes

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