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On the non-abelian Hodge locus I (2305.00943v1)
Published 1 May 2023 in math.AG and math.GT
Abstract: We partially resolve conjectures of Deligne and Simpson concerning $\mathbb Z$-local systems on quasi-projective varieties that underlie a polarized variation of Hodge structure. For local systems of "compact type", we prove (1) a relative form of Deligne's finiteness theorem, for any family of quasi-projective varieties, and (2) algebraicity of the corresponding non-abelian Hodge locus.
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