The relative Riemann-Roch theorem from Hochschild homology
arXiv:math/0603127
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].
77 pages. Completely rewritten and reorganized. Much more detailed than the previous version
References in corpus (3)
Cited by in corpus (19)
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- The Hochschild-Kostant-Rosenberg isomorphism for quantized analytic cycles
- Bivariance, Grothendieck duality and Hochschild homology, II: the fundamental class of a flat scheme-map
- Loop Spaces and Langlands Parameters
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- A variant of the Mukai pairing via deformation quantization
- Remarks on derived equivalences of Ricci-flat manifolds
- Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfaces
- The Ext algebra of a quantized cycle
- Modèles géométriques attachés aux paires réductives