Perverse sheaves on semi-abelian varieties

TL;DR

This paper characterizes complex perverse sheaves on semi-abelian varieties via their cohomology jump loci, extending previous results on abelian varieties and affine tori, with applications to algebraic geometry and topology.

Contribution

It provides a complete global characterization of perverse sheaves on semi-abelian varieties, generalizing earlier work and applying to various geometric and topological contexts.

Findings

Characterization of perverse sheaves via cohomology jump loci

Extension of Schnell's and Gabber-Loeser's results

Applications to Albanese map and homological duality

Abstract

We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on perverse sheaves on complex abelian varieties, as well as Gabber-Loeser's results on perverse sheaves on complex affine tori. We apply our results to the study of cohomology jump loci of smooth quasi-projective varieties, to the topology of the Albanese map, and in the context of homological duality properties of complex algebraic varieties.