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The nonabelian Hodge correspondence for vector bundles over noncompact curvesis adequately described by implementing a weighted filtration on the objectsinvolved. In order to establish a full correspondence between a Dolbeault and ade Rham space for a general complex reductive group $G$, we introduce torsorsgiven by parahoric group schemes in the sense of Bruhat--Tits. Combined withexisting results on the Riemann--Hilbert correspondence for logarithmicparahoric connections, this gives a full nonabelian Hodge correspondence fromHiggs bundles to fundamental group representations over a noncompact curvebeyond the $\text{GL}_n(\mathbb{C})$-case.

Tame parahoric nonabelian Hodge correspondence on curves