##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Peter Wear

#### UCSD

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

##### Abstract:

Deligne's weight-monodromy conjecture gives control over the zeros of local factors of L-functions of varieties at places of bad reduction. His proof in characteristic p was a step in his proof of the generalized Weil conjectures. Scholze developed the theory of perfectoid spaces to transfer Deligne's proof to characteristic 0, proving the conjecture for complete intersections in toric varieties. Building on Scholze's techniques, we prove the weight-monodromy conjecture for complete intersections in abelian varieties.

Advisor: Kiran Kedlaya

### May 29, 2020

### 10:00 AM

### Contact Peter Wear for Zoom link

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