Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free

Details Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free

2010-04-03

arxiv.org/abs/1004.0471v2

Mathematics

Commutative Algebra

Some statements/typos fixed thanks to corrections from the referees, main results remain the same

Scientific paper

Let (R,m) be a local ring and U_R=Spec(R) -{m} be the punctured spectrum of R. Gabber conjectured that if R is a complete intersection of dimension 3, then the abelian group Pic(U_R) is torsion-free. In this note we prove Gabber's statement for the hypersurface case. We also point out certain connections between Gabber's Conjecture, Van den Bergh's notion of non-commutative crepant resolutions and some well-studied questions in homological algebra over local rings.

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