Perfect-Prismatic F-Crystals and p-adic Shtukas in Families

TL;DR

This paper establishes an equivalence between perfect prismatic F-crystals and p-adic shtukas, linking formal and analytic Frobenius-linear objects over p-complete rings, with applications to prismatic cohomology of complex algebraic varieties.

Contribution

It proves an equivalence between categories of perfect prismatic F-crystals and p-adic shtukas without relying on Frobenius structures, extending the theory to broader settings.

Findings

Established a categorical equivalence between prismatic F-crystals and p-adic shtukas.

Extended the framework to arbitrary p-complete rings and affine-flat group schemes.

Applied results to prismatic cohomology of K3 surfaces and complete intersections.

Abstract

We show an equivalence between the two categories in the title, thus establishing a link between Frobenius-linear objects of formal (schematic) and analytic (adic) nature. We will do this for arbitrary p-complete rings, arbitrary affine-flat group schemes and without making use of the Frobenius structure. As a possible application, we take a look at prismatic cohomology of K3-surfaces and complete intersections of projective space.