Essential dimension via prismatic cohomology

Abstract: Let A be a complex abelian variety. Using prismatic cohomology, we show that for all but finitely many primes p, the multiplication-by-p cover p:A\to A is p-incompressible, as conjectured by Brosnan. As an application, we obtain new p-incompressibility results for congruence covers of Shimura varieties, extending previous work of Farb-Kisin-W, Brosnan-Fakhruddin, and Fakhruddin-Saini. This is joint work with Benson Farb and Mark Kisin.

algebraic geometrygroup theorynumber theoryrepresentation theory

Audience: researchers in the topic

Algebraic groups and algebraic geometry: in honor of Zinovy Reichstein's 60th birthday