Split Reductions of Simple Abelian Varieties

JOINT IAS/PU NUMBER THEORY SEMINAR
Topic:Split Reductions of Simple Abelian Varieties
Speaker:David Zywina
Affiliation:University of Pennsylvania
Date:Thursday, April 15
Time/Room:4:30pm - 5:30pm/Fine Hall -- 214

To an abelian variety over a number field one can associate an abelian variety to each prime ideal p of good reduction by reducing the variety modulo p . The geometry of these reductions need not resemble the geometry of the original abelian variety; for example, there are absolutely simple abelian varieties of dimension 2 whose reductions modulo p always split as a product of elliptic curves. In this talk, we shall describe progress on a conjecture of Murty and Patankar which predicts exactly which absolutely simple abelian varieties have reductions modulo p that are also absolutely simple.