##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Peter Wear

#### UCSD

## Perfectoid covers of abelian varieties and the weight-monodromy conjecture

##### Abstract:

The theory of perfectoid spaces was initially developed by Scholze to prove new cases of the weight-monodromy conjecture. He constructed perfectoid covers of toric varieties that allowed him to translate results from characteristic p to characteristic 0. We will give an overview of Scholze's method, then explain how to use an analogous construction for abelian varieties to prove the weight-monodromy conjecture for complete intersections in abelian varieties.

### October 31, 2019

### 2:00 PM

### AP&M 7321

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