Perverse sheaves on semi-abelian varieties
arXiv:1804.05014
Abstract
We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on perverse sheaves on complex abelian varieties, as well as Gabber-Loeser's results on perverse sheaves on complex affine tori. We apply our results to the study of cohomology jump loci of smooth quasi-projective varieties, to the topology of the Albanese map, and in the context of homological duality properties of complex algebraic varieties.
arXiv comment34 pages; comments are very welcome; v2: shortened several proofs, updated references, fixed typos
References in corpus (8)
- Wild Harmonic Bundles and Wild Pure Twistor D-modules
- Vanishing Theorems for constructible Sheaves on Abelian Varieties
- Perverse sheaves on semiabelian varieties
- Cohomology jump loci of differential graded Lie algebras
- Local systems on complements of arrangements of smooth, complex algebraic hypersurfaces
- Degenerate Perverse Sheaves on Abelian Varieties
- Aspherical Kähler Manifolds with Solvable Fundamental Group
- Remarks on the nonvanishing of cohomology groups for perverse sheaves on abelian varieties