Generalized Beauville decompositions
组织者
黄鹏飞
,
苏桃
, 孙浩
演讲者
訚琪峥
时间
2024年04月24日 16:00 至 17:00
地点
A3-2-303
线上
Zoom 242 742 6089
(BIMSA)
摘要
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.