New York Journal of Mathematics
Volume 14 (2008) 643-717


Ajay C. Ramadoss

The relative Riemann-Roch theorem from Hochschild homology

Published: October 30, 2008
Keywords: Riemann-Roch theorem, Mukai pairing, Hochschild-Kostant-Rosenberg map
Subject: 19L10, 16E40, 14F40

This paper attempts to clarify a preprint of Markarian (2001). Markarian's preprint proves the relative Riemann-Roch theorem using a result describing how the HKR map fails to respect comultiplication. This paper elaborates on the core computations in Markarian's preprint. These computations show that the HKR map twisted by the square root of the Todd genus "almost preserves" the Mukai pairing. This settles a part of a conjecture of Caldararu, 2005. The relative Riemann-Roch theorem follows from this and a result of Caldararu, preprint, 2003.

Author information

Department of Mathematics, University of Oklahoma, 621 Elm Avenue, Norman, OK-73019