Constructing Abelian Varieties over Qbar Not Isogenous to a Jacobian

JOINT IAS/PU NUMBER THEORY SEMINAR
Topic:Constructing Abelian Varieties over Qbar Not Isogenous to a Jacobian
Speaker:Jacob Tsimerman
Affiliation:Prirnceton University
Date:Thursday, October 28
Time/Room:4:30pm - 5:30pm/Fine Hall -- 214

We discuss the following question of Nick Katz and Frans Oort: Given an Algebraically closed field K , is there an Abelian variety over K of dimension g which is not isogenous to a Jacobian? For K the complex numbers its easy to see that the answer is yes for g>3 using measure theory, but over a countable field like Qbar new methods are required. Building on work of Chai-Oort, we show that, as expected, such Abelian varieties exist for K=Qbar and g>3 . We will explain the proof as well as its connection to the Andre Oort conjecture.