Dualizable abelian fibrations

TL;DR

This paper explores dualizable abelian fibrations, establishing a framework that reveals rich structures in their decomposition theorem and cohomology, with recent progress and applications in the context of the Langlands program.

Contribution

It introduces a new framework for dualizable abelian fibrations, advancing understanding of their decomposition and cohomological properties in algebraic geometry.

Findings

Framework for dualizable abelian fibrations established

Enhanced understanding of decomposition theorem structures

Applications to Langlands program progress

Abstract

In his proof of the fundamental lemma of the Langlands program, Ng\^o 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.