A primitive purity theorem for Frobenius modules

Abstract: In p-adic Hodge theory, a fundamental observation of Breuil and Kisin is that some Galois representations over p-adic integers give rise to interesting integral linear-algebraic data, where the latter nowadays are called Breuil--Kisin modules. The notion naturally generalizes to modules with Frobenius structures over a more general base, thanks to the prismatic cohomology introduced by Bhatt and Scholze. In this talk, we show that Frobenius modules over a regular ring admit a primitive purity theorem, and explain its potential application to p-adic local systems.

algebraic geometrynumber theory

Audience: researchers in the discipline

MIT number theory seminar

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