##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## David Hansen

## Duality and the p-adic Jacquet-Langlands correspondence

##### Abstract:

In joint work with Lucas Mann, we establish several new properties of the p-adic Jacquet-Langlands functor defined by Scholze in terms of the cohomology of the Lubin-Tate tower. In particular, we prove a duality theorem, establish bounds on Gelfand-Kirillov dimension, prove some non-vanishing results, and show a kind of partial Künneth formula. The key new tool is the six functor formalism with solid almost $\mathcal{O}^+/p$-coefficients developed recently by Mann.

### April 7, 2022

### 2:00 PM

APM 6402 and Zoom;

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

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