Number Theory Seminar

Speaker: Raju Krishnamoorthy (University of Georgia)

Title: Rank 2 local systems and abelian varieties

Abstract: 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 recent resolution of the p-adic companions conjecture may be used to approach the conjecture. This is joint work with A. Pál.