##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Claudius Heyer

#### University of Münster

## The left adjoint of derived parabolic induction

##### Abstract:

Recent advances in the theory of smooth mod $p$ representations of a $p$-adic reductive group $G$ involve more and more derived methods. It becomes increasingly clear that the proper framework to study smooth mod $p$ representations is the derived category $D(G)$.

I will talk about smooth mod $p$ representations and highlight their shortcomings compared to, say, smooth complex representations of $G$. After explaining how the situation improves in the derived category, I will spend the remaining time on the left adjoint of the derived parabolic induction functor.

### January 20, 2022

### 2:00 PM

Pre-talk at 1:30 PM

Zoom; see https://www.math.ucsd.edu/~nts

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