Deformation quantization in algebraic geometry

By Amnon Yekutieli. 2003

86 citations recorded by the source corpus.

Abstract We study deformation quantizations of the structure sheaf O X 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 O X (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7583f57a09a6e632820c55397c4d4c5e9af39427

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In Algebra and Number Theory

1. B. Tsygan
2. R. Nest
3. A. Gorokhovsky
4. P. Bressler
5. Kalle Karu
6. M. Gualtieri

In Mathematical Physics

1. B. Tsygan
2. R. Nest
3. A. Gorokhovsky
4. P. Bressler
5. M. Gualtieri
6. Christian Voigt
7. T. Voronov

In Statistical and Nonlinear Physics

1. B. Tsygan
2. R. Nest
3. A. Gorokhovsky
4. P. Bressler
5. T. Voronov

Citations in the corpus

• Deformation quantization of gerbes (2005, methodology): “Note that De Rham–Sullivan forms were used in [43] to classify deformation quantizations of algebraic varieties.”
• Fedosov quantization in positive characteristic (2005, unknown): “[BK1], [ Y ], and an earlier paper [NT] for the holomorphic situation).”