A variant of the Mukai pairing via deformation quantization

Abstract

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.

8 pages. Comments and suggestions welcome

References in corpus (2)

• The relative Riemann-Roch theorem from Hochschild homology
• Cyclic Cohomology of the Weyl Algebra

Cited by in corpus (3)

• Formality and Kontsevich--Duflo type theorems for Lie pairs
• The Hochschild-Kostant-Rosenberg isomorphism for quantized analytic cycles
• An index theorem for Lie algebroids