Corrigendum to “Deformation quantization in algebraic geometry”[Adv. Math. 198 (2005) 383--432] Academic Article uri icon


  • This note contains a correction of the proofs of the main results of [3], 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 [2]. 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

publication date

  • January 1, 2008