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arXiv · 1111.4947

Vanishing Theorems for constructible Sheaves on Abelian Varieties

Thomas Krämer·Rainer Weissauer
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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.

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Thomas Krämer, Rainer Weissauer. 2011-11-21. Vanishing Theorems for constructible Sheaves on Abelian Varieties. https://doi.org/10.1090/jag/645

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