BIMSA > GRASP seminar Generalized Beauville decompositions
Generalized Beauville decompositions
Organizers
Pengfei Huang , Tao Su , Hao Sun
Speaker
Qizheng Yin
Time
Wednesday, April 24, 2024 4:00 PM - 5:00 PM
Venue
A3-2-303
Online
Zoom 242 742 6089 (BIMSA)
Abstract
This serves as a complement to Junliang Shen’s talk. I will begin with the classical theory of the Beauville decomposition, which provides a canonical, multiplicative splitting of the Leray filtration for abelian schemes. Then I will discuss the problem of extending the Beauville decomposition to certain abelian fibrations with singular fibers. I will explain how the extension leads to the multiplicativity of the perverse (Leray) filtration for such fibrations, and eventually to a new proof of the P = W conjecture. Further results and open questions will also be discussed. Joint work with Younghan Bae, Davesh Maulik, and Junliang Shen.