Riemann-Roch theorems via deformation quantization, I

P. Bressler; R. Nest; B. Tsygan

doi:10.1006/aima.2000.1977

Riemann-Roch theorems via deformation quantization, I

P. Bressler^*, R. Nest, B. Tsygan

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We deduce the Riemann-Roch type formula expressing the microlocal Euler class of a perfect complex of D-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization. The proof of the latter is contained in the sequel to this paper.

Original language	English (US)
Pages (from-to)	1-25
Number of pages	25
Journal	Advances in Mathematics
Volume	167
Issue number	1
DOIs	https://doi.org/10.1006/aima.2000.1977
State	Published - Apr 15 2002

ASJC Scopus subject areas

General Mathematics

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10.1006/aima.2000.1977

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abstract = "We deduce the Riemann-Roch type formula expressing the microlocal Euler class of a perfect complex of D-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization. The proof of the latter is contained in the sequel to this paper.",

author = "P. Bressler and R. Nest and B. Tsygan",

note = "Funding Information: 1Current address: University of Arizona, Tucson, Arizona 85721. 2The third author was supported in part by NSF Grant DMS-9504522. Current Northwestern University, Evanston, Illinois 60208. E-mail: tsygan math.nwu.edu.",

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AU - Nest, R.

AU - Tsygan, B.

N1 - Funding Information: 1Current address: University of Arizona, Tucson, Arizona 85721. 2The third author was supported in part by NSF Grant DMS-9504522. Current Northwestern University, Evanston, Illinois 60208. E-mail: tsygan math.nwu.edu.

PY - 2002/4/15

Y1 - 2002/4/15

N2 - We deduce the Riemann-Roch type formula expressing the microlocal Euler class of a perfect complex of D-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization. The proof of the latter is contained in the sequel to this paper.

AB - We deduce the Riemann-Roch type formula expressing the microlocal Euler class of a perfect complex of D-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization. The proof of the latter is contained in the sequel to this paper.

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Riemann-Roch theorems via deformation quantization, I

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