Generic vanishing for semi-abelian varieties and integral Alexander modules

TL;DR

This paper extends generic vanishing theorems to semi-abelian varieties with applications to the finiteness of integral Alexander modules, offering new insights into the topology of complex algebraic varieties.

Contribution

It generalizes generic vanishing results to semi-abelian varieties and establishes finiteness properties for integral Alexander modules of complex varieties.

Findings

Finiteness of integral Alexander modules for varieties mapping to semi-abelian varieties

Extension of generic vanishing theorems to broader class of varieties

Topological applications in complex algebraic geometry

Abstract

We revisit generic vanishing results for perverse sheaves with any field coefficients on a complex semi-abelian variety, and indicate several topological applications. In particular, we obtain finiteness properties for the integral Alexander modules of complex algebraic varieties mapping to semi-abelian varieties. Similar results were recently derived by the authors by using Morse-theoretic arguments.