Mathematics > Algebraic Geometry
arXiv:2606.22637 (math)
[Submitted on 21 Jun 2026]
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.
Submission history
From: Haoyang Guo [view email]
[v1]
Sun, 21 Jun 2026 18:51:22 UTC (107 KB)
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