Perverse sheaves on semi-abelian varieties

We give a complete (global) characterization of $${\mathbb {C}}$$ -perverse sheaves on semi-abelian varieties in terms their cohomology jump loci. Our results generalize Schnell’s work perverse complex abelian varieties, as well Gabber–Loeser’s affine tori. apply our to the study loci smooth quasi-projective topology Albanese map, and context homological duality properties algebraic varieties.