English

Perverse sheaves on semi-abelian varieties

Algebraic Geometry 2020-11-26 v3

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.

Keywords

Cite

@article{arxiv.1804.05014,
  title  = {Perverse sheaves on semi-abelian varieties},
  author = {Yongqiang Liu and Laurentiu Maxim and Botong Wang},
  journal= {arXiv preprint arXiv:1804.05014},
  year   = {2020}
}

Comments

34 pages; comments are very welcome; v2: shortened several proofs, updated references, fixed typos

R2 v1 2026-06-23T01:23:07.520Z