中科院数学与系统科学研究院

数学研究所

代数几何研讨班

报告人：訚琪峥（北京大学）

题  目：Abelian fibrations, Perverse = Chern, and multiplicativity

时  间：2023.09.26（星期二），14:00-15:00

地  点：南楼 913

摘 要：The perverse filtration captures interesting homological information of algebraic maps. Recent studies of the Hitchin and Beauville-Mukai integrable systems suggest two common features of the perverse filtration for 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 statements 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 with Davesh Maulik and Junliang Shen.