##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Jake Postema

#### UC San Diego

## Higher Smooth Duals for Mod p Representations of Algebraic Groups

##### Abstract:

The Local Langlands program and its variants have lead to the study of smooth, admissible representations of p-adic algebraic groups. The degree to which these are understood depends on the field over which the representations are being taken. Over a field of characteristic p, the usual dual in the category of smooth representations gives less information: in most cases of interest, it is 0! Kohlhaase has defined candidates-the higher duality functors-for a useful replacement. We will go over their properties, and some examples in rank one where they can be computed.

Host: Number Theory Group

### March 14, 2019

### 2:00 PM

### AP&M 7321

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