Vanishing theorems for perverse sheaves on abelian varieties, revisited

Bhargav Bhatt; Christian Schnell; Peter Scholze

doi:10.1007/s00029-017-0377-8

Vanishing theorems for perverse sheaves on abelian varieties, revisited

Bhargav Bhatt
, Christian Schnell
, Peter Scholze

Mathematics

University of Michigan, Ann Arbor
University of Bonn

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We revisit some of the basic results of generic vanishing theory, as pioneered by Green and Lazarsfeld, in the context of constructible sheaves. Using the language of perverse sheaves, we give new proofs of some of the basic results of this theory. Our approach is topological/arithmetic, and avoids Hodge theory.

Original language	English
Pages (from-to)	63-84
Number of pages	22
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00029-017-0377-8
State	Published - Mar 1 2018

Keywords

Abelian varieties
Formality
Fourier transform
Generic vanishing
Hard Lefschetz
Perverse sheaves
Weights

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10.1007/s00029-017-0377-8

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KW - Formality

KW - Fourier transform

KW - Generic vanishing

KW - Hard Lefschetz

KW - Perverse sheaves

KW - Weights

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Vanishing theorems for perverse sheaves on abelian varieties, revisited

Abstract

Keywords

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