Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Vanishing theorems for constructible sheaves on abelian varieties


Authors: Thomas Krämer and Rainer Weissauer
Journal: J. Algebraic Geom. 24 (2015), 531-568
DOI: https://doi.org/10.1090/jag/645
Published electronically: April 20, 2015
MathSciNet review: 3344764
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Abstract | References | Additional Information

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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Additional Information

Thomas Krämer
Affiliation: Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Address at time of publication: Centre de Mathématiques Laurent Schwartz, École Polytechnique, F-91128 Palaiseau cedex, France
Email: tkraemer@mathi.uni-heidelberg.de, thomas.kraemer@polytechnique.edu

Rainer Weissauer
Affiliation: Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: weissauer@mathi.uni-heidelberg.de

DOI: https://doi.org/10.1090/jag/645
Received by editor(s): September 12, 2012
Received by editor(s) in revised form: June 9, 2013
Published electronically: April 20, 2015
Article copyright: © Copyright 2015 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society