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Pré-Publication, Document De Travail Année : 2022

$L^2$ Cohomology of a Variation of Hodge structure for an infinite covering of an open curve ramified at infinity

Bastien Jean
  • Fonction : Auteur

Résumé

Let $X$ be a compact Riemann surface, $\Sigma$ a finite set of points and $M = X\setminus \Sigma$. We study the $L^2$ cohomology of a polarized complex variation of Hodge structure on a Galois covering of the Riemann surface of finite type $M$. In this article we treat the case when the covering comes from a branched covering of $X$, and where $M$ is endowed with a metric asymptotic to a Poincar\'e metric. We prove that after tensorisation with the algebra of affiliated operators, the $L^2$ cohomology admits a pure Hodge structure.

Dates et versions

hal-03877952 , version 1 (29-11-2022)

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Citer

Bastien Jean. $L^2$ Cohomology of a Variation of Hodge structure for an infinite covering of an open curve ramified at infinity. 2022. ⟨hal-03877952⟩

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