Perverse sheaves on semiabelian varieties

Abstract

We give a Tannakian description for categories of l-adic perverse sheaves on semiabelian varieties which combines a construction of Gabber and Loeser for algebraic tori with a generic vanishing theorem for the cohomology of constructible sheaves on abelian varieties. As an application we explain how the arising Tannaka groups on abelian varieties can be studied in terms of semiabelian degenerations via the functor of nearby cycles.

14 pages

References in corpus (2)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• Holonomic D-modules on abelian varieties

Cited by in corpus (9)

• Semisimple Super Tannakian Categories with a small Tensor Generator
• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• Perverse sheaves on semi-abelian varieties
• Generic vanishing for semi-abelian varieties and integral Alexander modules
• Summands of theta divisors on Jacobians
• Mellin transformation, propagation, and abelian duality spaces
• Characteristic classes and Hilbert-Poincaré series for perverse sheaves on abelian varieties
• Non-abelian Mellin Transformations and Applications
• Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution