# Tannakian Categories attached to abelian Varieties

## TL;DR

This paper constructs a semisimple super-Tannakian category from specific perverse sheaves on abelian varieties, including intersection cohomology sheaves of curves and smooth ample divisors.

## Contribution

It introduces a new categorical framework linking perverse sheaves on abelian varieties to Tannakian categories, expanding the understanding of their geometric and algebraic structures.

## Key findings

- Construction of a semisimple super-Tannakian category from perverse sheaves
- Inclusion of intersection cohomology sheaves of curves and ample divisors
- Establishment of categorical properties related to abelian varieties

## Abstract

Starting from certain perverse sheaves on an abelian variety, including the intersection cohomology sheaves of curves and smooth ample divisors, we construct a semisimple super-Tannakian category.