Degenerate Perverse Sheaves on Abelian Varieties

Abstract

We analyze irreducible perverse sheaves on abelian varieties, defined over the complex numbers or the algebraic closure of a finite field, whose Euler characteristic is zero. We give a description of such perverse sheaves under assumptions for the case of simple abelian varieties.

version2: appendix added version3: The appendix from the paper "Why certain Tannaka groups attached to abelian varieties are almost connected" has now been moved to become an appendix of this paper

References in corpus (6)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• On Subvarieties of Abelian Varieties with degenerate Gauss mapping
• Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong)
• A Remark on Rigidity of BN-sheaves
• Why certain Tannaka groups attached to abelian varieties are almost connected
• On the Rigidity of BN-sheaves

Cited by in corpus (8)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• Characteristic cycles and the microlocal geometry of the Gauss map, II
• Perverse sheaves on semi-abelian varieties
• Why certain Tannaka groups attached to abelian varieties are almost connected
• Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollár
• Holonomic complexes on abelian varieties, Part I
• Holonomic D-modules on abelian varieties
• Vanishing theorems for abelian varieties over finite fields