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

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arxiv 2305.09741 v1 pith:7CLMCDMG submitted 2023-05-16 math.AG math.CV

Yohan Brunebarbe This is my paper · ORCID
classification math.AGmath.CV
keywords analyticcomplexconnectednormalrepresentationsemisimplespacealgebraic
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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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  1. O-minimal geometry of higher Albanese manifolds

    math.AG 2025-05 conditional novelty 8.0 of 10

    Higher Albanese manifolds and maps are definable in o-minimal structures, and if a higher Albanese manifold of level at least three is algebraic, the tower stabilises at step two, making the pro-unipotent fundamental ...

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