Fedosov quantization in algebraic context

Abstract

We consider the problem of quantization of smooth symplectic varieties in the algebro-geometric setting. We show that, under appropriate cohomological assumptions, the Fedosov quantization procedure goes through with minimal changes. The assumptions are satisfied, for example, for affine and for projective varieties. We also give a classification of all possible quantizations.

46 pages, Latex2e, version 4 and final. Corrected some imprecise statements, added some remarks on canonical quantization

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