The relative Riemann-Roch theorem from Hochschild homology
Algebraic Geometry
2008-10-31 v5
Abstract
This write up attempts to clarify a preprint by Markarian [2] which proves This paper attempts to clarify a preprint of Markarian [2]. The preprint by Markarian [2] 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 [2]. 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[3]. The relative Riemann-Roch theorem follows from this and a result of Caldararu[4].
Keywords
Cite
@article{arxiv.math/0603127,
title = {The relative Riemann-Roch theorem from Hochschild homology},
author = {Ajay C. Ramadoss},
journal= {arXiv preprint arXiv:math/0603127},
year = {2008}
}
Comments
77 pages. Completely rewritten and reorganized. Much more detailed than the previous version