Dualizable abelian fibrations

Abstract

In his proof of the fundamental lemma of the Langlands program, Ngô initiated the study of the decomposition theorem for abelian fibrations. When an abelian fibration admits a duality structure, the decomposition theorem and the perverse filtration on cohomology exhibit rich structures. The purpose of these notes is to describe a framework for dualizable abelian fibrations and to discuss some recent progress and applications.

25 pages. Submitted to the Proceedings of the 2025 Summer Research Institute in Algebraic Geometry