  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.
