Deformation quantization in algebraic geometry

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Abstract

We study deformation quantizations of the structure sheaf OX of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of OX (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.

Original languageEnglish
Pages (from-to)383-432
Number of pages50
JournalAdvances in Mathematics
Volume198
Issue number1 SPEC. ISS.
DOIs
StatePublished - 1 Dec 2005

Keywords

  • DG Lie algebras
  • Deformation quantization
  • Formal geometry
  • Noncommutative algebraic geometry

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