Erratum to: Deformation Quantization in Algebraic Geometry Academic Article uri icon


  • This note contains a correction of the proofs of the main results of [Ye1], namely Theorems 0.1 and 0.2. The results are correct as originally stated. The mistake in my original proofs was discovered Michel Van den Bergh, and I thank him for calling my attention to it. The way to fix the proofs is essentially contained in his paper [VdB]. Let me begin by explaining the mistake. As can be seen in Example 0.1 below, the mistake itself is of a rather elementary nature, but it was obscured by the complicated context. Suppose K is a field of characteristic 0, and X is a smooth separated n-dimensional scheme over K. Recall that the coordinate bundle CoorX is an infinite dimensional bundle over X, with free action by the group GLn,K. The quotient bundle is by definition … (πgl∗ ΩCoor X)GLn(K) = ΩLCC X … From that I deduced (incorrectly, top of page 424) that the Maurer-Cartan form ωMC is a global section of the sheaf … Ω1 LCC X ̂⊗OLCC X …

publication date

  • January 1, 2007

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