Prismatic crystals and p-adic Riemann--Hilbert correspondence

2024/11/27 by Hui Gao, Min Yu, Gao, Hui +3
Mathematics · #advanced mathematical theories #Advanced Algebra and Geometry #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2411.18780

Abstract

We systematically study relative and absolute Δ_dR⁺-crystals on the (log-) prismatic site of a smooth (resp.~ semi-stable) formal scheme. Using explicit computation of stratifications, we classify (local) relative crystals by certain nilpotent connections, and classify (local) absolute crystals by certain enhanced connections. By using a p-adic Riemann--Hilbert functor and an infinite dimensional Sen theory over the Kummer tower, we globalize the results on absolute crystals and further classify them by certain small (global) \mathbbB_dR⁺-local systems.

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