# Real structures on ordinary Abelian varieties

 Joint IAS/Princeton University Number Theory Seminar Topic: Real structures on ordinary Abelian varieties Speaker: Mark Goresky Affiliation: Member, School of Mathematics Date: Thursday, March 2 Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University

The "moduli space" for principally polarized complex $n$ dimensional Abelian varieties with real structure (that is, anti-holomorphic involution) may be identified with a certain locally symmetric space for the group $\mathrm{GL}(n)$ over the real numbers. Is it possible to make sense of the points of this space over a finite field? This talk describes joint work with Yung-sheng Tai (Haverford College) in which we propose an approach to this question for ordinary Abelian varieties.