Prof. Dr. Qizheng Yin (Beijing University)
Abelian fibrations, Perverse = Chern, and multiplicativity abstract
Abstract:
The perverse filtration captures interesting homological information of algebraic maps. Recent studies of integrable systems (e.g. Hitchin systems, Beauville-Mukai systems) suggest two common features of the perverse filtration of abelian fibrations:1) the perverse filtration is multiplicative with respect to the cup product;2) the perversity of tautological classes is governed by the Chern degree.In this talk, I will explain a unified approach to both 1) and 2) for a natural class of abelian fibrations, namely fibrations in compactified Jacobians. I will discuss several ingredients from (coherent) derived categories, K-theory/Chow theory, and constructible categories, as well as some applications of our result. Joint work in progress with Davesh Maulik and Junliang Shen.
16:00 • ETH Zentrum, Building ITS, Room