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arXiv · 2608.26393

Isocrystals on unibranch varieties and open immersions

Adrian Langer·Lei Zhang
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Abstract

We prove that for a connected, geometrically unibranch variety $X$ over a perfect field of positive characteristic and a dense open subset $U \subset X$, the canonical homomorphism between the Tannaka duals of the categories of overconvergent isocrystals is a quotient map. We also show that the analogous statement for convergent isocrystals, and for all isocrystals, fails. The counterexample is based on Crew's construction of a unit-root $F$-isocrystal that is convergent but not overconvergent.

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Adrian Langer, Lei Zhang. 2026-08-26. Isocrystals on unibranch varieties and open immersions. https://arxiv.org/abs/2608.26393

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