Vanishing theorems for perverse sheaves on abelian varieties, revisited

2017/02/21 by Bhatt, Bhargav, Schnell, Christian, Scholze, Peter · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.06395

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.

Cited by

• Generic vanishing on homogeneous spaces in arbitrary characteristic

Related

• Applications of perverse sheaves in commutative algebra
• Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves
• Vanishing theorems for abelian varieties over finite fields
• A derived category approach to generic vanishing
• Degenerate Perverse Sheaves on Abelian Varieties