Abelian varieties not isogenous to Jacobians
Abelian varieties not isogenous to Jacobians

Jacob Tsimerman, University of Toronto
IAS  Simonyi Hall Seminar Room SH101
InPerson and Online Talk
Zoom link: https://princeton.zoom.us/j/97126136441
Passcode: The three digit integer that is the cube of the sum of its digits
Katz and Oort raised the following question: Given an algebraically closed field k, and a positive integer g>3, does there exist an abelian variety over k not isogenous to a Jacobian over k? There has been much progress on this question, with several proofs now existing over \overline{\mathbb{Q}}. We discuss recent work with Ananth Shankar, answering this question in the affirmative over \overline{\mathbb{F}_q(T)}. Our method introduces new types of local obstructions, and can be used to give another proof over \overline{\mathbb{Q}}.