We give a complete (global) characterization of \({\mathbb {C}}\)-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.

中文翻译：

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不规则的滑轮在半亚伯利亚品种上

我们用半同型变种的同调跃迁基因座给出了\（{\ mathbb {C}} \）-正交滑轮的完整（全局）表征。我们的结果概括了Schnell在复杂的阿贝尔变种上的反滑轮的工作，以及Gabber-Loeser在复杂的仿射花托上的反滑轮的结果。我们将我们的结果应用于光滑拟射影变种的同调跃迁轨迹研究，Albanese图的拓扑以及复杂代数变种的同构对偶性质。