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arXiv · 2609.39815

Potential isotriviality of isocrystals and proper covers

Adrian Langer·Lei Zhang
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Abstract

We study convergent and overconvergent isocrystals that become trivial after pullback along a proper surjective morphism. On a geometrically unibranch variety over an algebraically closed field, every such object is already trivialized by a finite étale cover. Over a perfect field, this shows that a proper cover giving geometric triviality can be replaced by a finite étale cover over the ground field, and implies finiteness of the geometric monodromy group. For proper geometrically unibranch varieties, finite geometric monodromy is also sufficient. In the overconvergent case, a dominant morphism can replace the given proper cover. A nodal curve shows why the geometrically unibranch hypothesis is needed.

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Adrian Langer, Lei Zhang. 2026-09-30. Potential isotriviality of isocrystals and proper covers. https://arxiv.org/abs/2609.39815

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