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arXiv · 2606.22637

Ogus's conjecture on F-isocrystals

Haoyang Guo
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Abstract

In 1984, Ogus conjectured the existence of a canonical F-isocrystal that enhances the Gauss--Manin connection, for a proper relative rigid space with analytically good reduction. We give a positive answer to this conjecture in full generality, through p-adic local systems and prismatic methods. Along the way, we introduce a prismatic refinement of the p-adic Riemann--Hilbert functor and prove a primitive purity theorem for Frobenius modules.

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Haoyang Guo. 2026-06-21. Ogus's conjecture on F-isocrystals. https://arxiv.org/abs/2606.22637

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