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

  • Part of
  • Hailong Dao
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 1 / January 2012
    Published online by Cambridge University Press:
    09 November 2011, pp. 145-152
    Print publication:
    January 2012
    • Article
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  • Let (R,m) be a Noetherian local ring and UR=Spec(R)−{m} be the punctured spectrum of R. Gabber conjectured that if R is a complete intersection of dimension three, then the abelian group Pic(UR) 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.