Vanishing theorems for abelian varieties over finite fields

TL;DR

This paper proves that the Euler-Poincare characteristic of perverse sheaves on abelian varieties over finitely generated fields is always non-negative, extending understanding of sheaf cohomology in algebraic geometry.

Contribution

It establishes a non-negativity result for Euler-Poincare characteristics of perverse sheaves on abelian varieties over finite fields, a new insight in algebraic geometry.

Findings

Euler-Poincare characteristic is non-negative for these sheaves

Extends known results to varieties over finitely generated fields

Provides a new vanishing theorem for perverse sheaves

Abstract

For perverse sheaves K on abelian varieties X defined over a finitely generated field F we prove that the Euler-Poincare characteristic (defined for the extension of K to the algebraic closure of F) is non-negative.