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arXiv · 2305.09741

Existence of the Shafarevich morphism for semisimple local systems on quasi-projective varieties

Yohan Brunebarbe
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Abstract

Let X be a normal connected complex algebraic variety equipped with a semisimple complex representation of its fundamental group. Then, under a maximality assumption, we prove that the covering space of X associated to the kernel of the representation has a proper surjective holomorphic map with connected fibres onto a normal analytic space with no positive-dimensional compact analytic subspace.

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Yohan Brunebarbe. 2023-05-16. Existence of the Shafarevich morphism for semisimple local systems on quasi-projective varieties. https://arxiv.org/abs/2305.09741

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