Independence of ℓ for Frobenius Conjugacy Classes Attached to Abelian Varieties - Rong Zhou

Explore a comprehensive lecture on the independence of ℓ for Frobenius conjugacy classes attached to abelian varieties, presented by Rong Zhou at the Institute for Advanced Study. Delve into advanced mathematical concepts, including Mumford-Tate groups, E-adic representations, and Deligne's Theorem. Examine the relationship between these concepts and Shimura varieties, and follow the intricate steps of the reduction process. Gain insights into the Second Main Theorem and its proof, with a focus on CM liftings and special points. Investigate compatible local systems and explicit curves in the special fiber of Shimura varieties. This in-depth, 69-minute talk provides a rigorous exploration of complex mathematical theories and their applications in the study of abelian varieties.

Intro
Structure of Talk
$i Mumford-Tate groups
E-adic representations
Deligne's Theorem
Previous work
Relationship with Shimura varieties
Reduction Step
Second Main Theorem
Idea of Proof of Theorem (2)
CM liftings 1: Special points
CM-liftings II: Serre-Tate canonical lift
Compatible local systems II
Explicit curves in the special fiber of Shimura varieties