Riemann-Roch theorems via deformation quantization. II
type: Item
instance of: scholarly article
title: Riemann-Roch theorems via deformation quantization. II
zbMATH Open document ID: 1021.53065
published in: Advances in Mathematics
publication date: 2002-07-04T00:00:00Z
review text: A deformation quantization of a complex manifold \(M\) is a formal one-parameter deformation of the structure sheaf \({\mathcal O}_M\), i.e., a sheaf of algebras \(A^t_M\) flat over \(\mathbb{C}t\) together with an isomorphism of algebras \(\psi: A^t_M\otimes_{\mathbb{C}t}\mathbb{C}\to {\mathcal O}_M\). The formula \(\{f,g\}={1\over t}[\widetilde f,\widetilde g]+ tA^t_M\), where \(f\), \(g\) are local sections of \({\mathcal O}_M\) and \(\widetilde f\), \(\widetilde g\) are their lifts to \(A^t_M\), defines a Poisson structures on \(M\) called the Poisson structure associated to the deformation quantization \(A^t_M\). A deformation quantization \(A^t_M\) is called symplectic if the associated Poisson structure is nondegenerate. The aim of this second part of the paper is to give a proof of a certain Riemann-Roch type theorem for symplectic deformations. For Part I, cf. ibid. 167, 1-25 (2002; Zbl 1021.53064).
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 58J20
zbMATH DE Number: 1763527
zbMATH Keywords: Riemann-Roch theorem
zbMATH Keywords: deformation quantization
author: Paul Bressler
author: Ryszard Nest
author: Boris Tsygan
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
full work available at URL: aima.2000.1978
OpenAlex ID: W2050015327
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DOI: 10.1006/AIMA.2000.1978
description: scientific article; zbMATH DE number 1763527