Research-Prismatic crystals and p-adic Riemann–Hilbert correspondence over imperfect residue fields

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Prismatic crystals and p-adic Riemann–Hilbert correspondence over imperfect residue fields

Speaker: Yimeng Tang（SUSTech）
Time: Oct 26, 2026, 15:00-16:00
Location: Room M3009, College of Science Building

Abstract

Let K be a CDVF of mixed characteristic (0,p), whose residue field admits a finite p-basis. Assuming that K is weakly unramified over its canonical subfield, we establish an equivalence between prismatic de Rham crystals on the absolute prismatic site of O_K and nearly de Rham representations of G_K. Both sides are classified by certain enhanced connections, with the Galois side described via a decompleted p-adic Riemann–Hilbert correspondence. In this talk, I will focus on representations, with C-coefficients, where C is the completed algebraic closure of K.