Abelian varieties not isogenous to Jacobians

Abelian varieties not isogenous to Jacobians

Jacob Tsimerman, University of Toronto
IAS - Simonyi Hall Seminar Room SH-101

In-Person 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}}.