 

Ajay C. Ramadoss
The relative RiemannRoch theorem from Hochschild homology


Published: 
October 30, 2008

Keywords: 
RiemannRoch theorem, Mukai pairing, HochschildKostantRosenberg map 
Subject: 
19L10, 16E40, 14F40 


Abstract
This paper attempts to clarify a preprint of Markarian (2001).
Markarian's preprint proves the relative RiemannRoch 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
RiemannRoch theorem follows from this and a result of Caldararu,
preprint, 2003.


Author information
Department of Mathematics, University of Oklahoma, 621 Elm Avenue, Norman, OK73019
aramadoss@math.ou.edu

