题目：Hodge, Tate and Mumford–-Tate conjectures

报告人：唐指朝（复旦大学）

时间：5月29日（周五）上午9：30-10：30

地点：数学科学学院308 

摘要：The Mumford–-Tate conjecture provides a bridge between the Hodge conjecture and the Tate conjecture. In this talk, we explore the history and relations between these conjectures and some recent progress in the case of hyper-K\ahler varieties. Several results concerning the Mumford--Tate conjecture for hyper-K\ahler varieties are established, where the main one is the conjecture for the semisimplified $\ell$-adic Galois representations attached to hyper-K\ahler varieties with second Betti number $b_2 \ge 4$.

The proofs rely on comparing the ranks of $\ell$-adic algebraic monodromy groups in higher degrees to those in degree $2$ via the theory of Frobenius tori and the Looijenga--Lunts--Verbitsky Lie algebra. 

This talk is based on a joint work with Haitao Zou.