##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Yuri Zarhin

#### Penn State University

## Tate and Weil classes on abelian varieties over finite fields

##### Abstract:

We discuss nontrivial multiplicative relations among eigenvalues of Frobenius endomorphisms of abelian varieties over finite fields. (The trivial relations are provided by the Riemann Hypothesis that was proven by A. Weil.) We classify all abelian varieties over finite fields of a certain dimension which admit the nontrivial relations and give an explicit construction of corresponding exotic Tate classes.

Host: Cristian Popescu

### May 7, 2015

### 2:00 PM

### AP&M 7321

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