Reconstruction of a Variety from 𝒪[[ℏ]]-Modules

Abstract

We prove that varieties are uniquely determined by the derived category of 𝒪[[ℏ]]-modules with coherent cohomology which is the same as 𝒪-modules proved by A. Bondal and D. Orlov. We also generalize a theorem of Orlov.

Key Words:

• Deformation quantization
• Fourier–Mukai transforms

2010 Mathematics Subject Classification:

• 32C38
• 46L65
• 53D55

ACKNOWLEDGMENTS

I would like to thank Pierre Schapira for useful Remarks.

Notes

Communicated by S. Bazzoni.