The relative Riemann-Roch theorem from Hochschild homology
By A. Ramadoss. 2006
52 citations recorded by the source corpus.
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].
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f5591028b3ae7ebf32cd19d0e2a275dcd5cff9a7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, methodology): “hern class of a coherent sheaf takes values in the Hodge cohomology ⊕ iHi(Ωi X ) (see also [27]). A new proof of this result was obtained in [44, 45] using an algebraic-differential calculus (see also [14, 50]). This latter approach emphasizes the importance of viewing the Chern character as a map to”
- Hochschild cohomology and Atiyah classes (2007, unknown): “g result Theorem 1.3. (see §9) The map in D(X) (1.1) TL poly(OX) HKR◦(td(L)1/2∧−) −−−−−−−−−−−−−→DL poly(OX) is an isomorphism of Gerstenhaber algebras in D(X). This result seems related to results in [5, 16, 19] although it does not appear in this form in these papers. Applying the hypercohomology f”
- The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem (2006, methodology): “Our definition of the global HKR isomorphism appeared in the preprint of the present paper and was used in [4, 13].”