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arXiv · 1503.04243

Convergent isocrystals on simply connected varieties

Hélène Esnault·Atsushi Shiho
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Abstract

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 \'etale fundamental group, any isocrystal on on $X/W$ is trivial. We prove this conjecture under two additional assumptions. Version 2: the main change is an addendum. We prove that if $X$ is a connected smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$ with trivial \'etale fundamental group, any infinitesimal isocrystal on $X/W$ is trivial. To this aim we wrote some general facts on such infinitesimal isocrystals over W which are missing in the literature.

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Hélène Esnault, Atsushi Shiho. 2015-03-13. Convergent isocrystals on simply connected varieties. https://arxiv.org/abs/1503.04243

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