Reflexive modules on normal surface singularities and representations of the local fundamental group |
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Authors: | Trond Stølen Gustavsen Runar Ile |
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Institution: | a Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway b Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway |
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Abstract: | We consider the Riemann-Hilbert correspondence on the complement of a normal surface singularity (X,x). Through a closure operation we obtain a correspondence between the category of finite dimensional representations of the local fundamental group and the category of left DX,x-modules that are reflexive as OX,x-modules. We show that under this correspondence profinite representations correspond to invariant modules and that these admit a canonical structure as left DX,x-modules. We prove that the fundamental module is an invariant module if and only if (X,x) is a quotient singularity. Finally we investigate some algebraisation aspects. |
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Keywords: | 32S40 13C14 32S05 |
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