## Algebra

•  Pavel Čoupek, MSU
•  Ramification bounds for mod p étale cohomology via prismatic cohomology
•  10/10/2022
•  3:00 PM - 4:00 PM
•  C304 Wells Hall
•  Preston Wake (wakepres@msu.edu)

Let $K/\bf{Q}_p$ be a local number field of absolute ramification index $e$, and let $X$ be a proper smooth $O_K$-scheme. I will discuss how one can obtain bounds on ramification of the mod $p$ Galois representations arising as the étale cohomology of (the geometric generic fiber of) $X$ in terms of $e$, the given prime $p>2$ and the cohomological degree $i$. The key tools for achieving this are the Breuil-Kisin and $A_{\rm inf}$-cohomology theories of Bhatt, Morrow and Scholze, and a series of conditions based on a criterion of Gee and Liu regarding crystallinity of the representation attached to a free Breuil-Kisin-Fargues $G_K$-module.

## Contact

Department of Mathematics
Michigan State University