Prismatic approach to crystalline local systems

Abstract: Let \(X\) be a smooth proper scheme over a \(p\)-adic field such that \(X\) has a good reduction. Inspired by the de Rham comparison theorem in complex geometry, Grothendieck asked if there is a "mysterious functor" relating étale cohomology of the generic fiber and crystalline cohomology of the special fiber. This question was answered by work of many people, including Fontaine and Faltings. In particular, this motivates the definition of a \(p\)-adic Galois representation being crystalline, generalizing the étale cohomology of \(X\) as above. In this talk, we will give an overview for the prismatic approach of Bhatt-Scholze on crystalline representations. Moreover, jointly with Emanuel Reinecke, we will consider the higher dimensional generalization of this approach on crystalline local systems.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID: 818 0595 3631

Zoom password: 746304

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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