Vanishing Theorems for constructible Sheaves on Abelian Varieties
Algebraic Geometry
2015-10-01 v6
Abstract
We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing theorem for a homomorphism between abelian varieties. Our proof relies on a Tannakian description for convolution products of perverse sheaves, and with future applications in mind we discuss the basic properties of the arising Tannaka groups.
Cite
@article{arxiv.1111.4947,
title = {Vanishing Theorems for constructible Sheaves on Abelian Varieties},
author = {Thomas Krämer and Rainer Weissauer},
journal= {arXiv preprint arXiv:1111.4947},
year = {2015}
}