## Speaker:

Raju Krishnamoorthy

## Institution:

University of Georgia

## Time:

Wednesday, February 6, 2019 - 3:00pm

## Location:

RH 306

Let X/k be a smooth variety over a finite field. Motivated by work of Corlette-Simpson over the complex numbers, we formulate a conjecture that certain rank 2 local systems on X come from families of abelian varieties. After an introduction to l/p-adic companions, we explain how the existence of a complete set of p-adic companions can be used to approach the conjecture. We also prove Lefschetz theorems for families of abelian varieties over F_q, analogous to work of Simpson over C. This is joint work with A. Pál.