Deformation quantization in algebraic geometry

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


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
Issue number1 SPEC. ISS.
StatePublished - 1 Dec 2005


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

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Deformation quantization in algebraic geometry'. Together they form a unique fingerprint.

Cite this