A prismatic Riemann-Hilbert correspondence

Abstract: Let k be a perfect field of characteristic p. For smooth k-schemes, Emerton and Kisin gave a contravariant Riemann-Hilbert correspondence describing constructible F_p sheaves using Frobenius modules, with a finiteness condition they call "finitely generated unit".

I will explain how to describe the derived category of constructible sheaves for a fixed normal crossings stratification in the logarithmic setting, using a new notion of finitely generated unit (varphi,Gamma) modules over a deperfected base. I globalize the correspondence using log prismatic crystals as developed by Koshikawa and Yao, and show various compatibilities such as perverse t-exactness and pushforward compatibility.

algebraic geometrynumber theory

Audience: researchers in the topic

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Boston University Number Theory Seminar