# Meeting Details

Title: Systems of $\ell$-adic representations arising from abelian varieties Algebra and Number Theory Seminar Yuri Zarhin, Penn State University Famous (and still unproven in full generality) conjectures of Serre-Grothendieck, Tate and Fontaine-Mazur describe $\ell$-adic representations that arise from the action of the absolute Galois group of a number field $K$ on the (twisted) $\ell$-adic cohomology groups of varieties that are defined over $K$. Assuming all these conjectures, we discuss the following question: which $\ell$-adic representations correspond to the $\ell$-adic Tate modules of an abelian variety? We give an answer for abelian varieties without complex multiplication. This is a report on a joint work with Stefan Patrikis (U of Utah) and Felipe Voloch (U of Texas, Austin).