##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Bao Le Hung

#### Northwestern

## Moduli of Fontaine-Laffaille modules and mod p local-global compatibility.

##### Abstract:

The mod p cohomology of locally symmetric spaces for definite unitary groups at infinite level is expected to realize the mod p local Langlands correspondence for $GL_n$. In particular, one expects the (component at p) of the associated Galois representation to be determined by cohomology as a smooth representation. I will describe how one can establish this expectation in many cases when the local Galois representation is Fontaine-Laffaille. \\ \\ This is joint work with D. Le, S. Morra, C. Park and Z. Qian.

Host: Kiran Kedlaya

### December 10, 2020

### 1:00 PM

### See https://www.math.ucsd.edu/\~{}nts/

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