The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem
By N. Markarian. 2006
106 citations recorded by the source corpus.
We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann–Roch theorem.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/eb0b04adf9ee3058d8495ce432e711c638ade36a
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In Geometry and Topology
- T. Bridgeland
- P. Aspinwall
- G. Moore
- Alexander Kuznetsov
- Yukinobu Toda
- A. Kapustin
- Emanuele Macrì
- K. Hori
In Mathematical Physics
- T. Bridgeland
- G. Moore
- Yukinobu Toda
- P. Aspinwall
- A. Kapustin
- Alexander Perry
- Emanuele Macrì
- Michael R Douglas
Citations in the corpus
- Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, background): “A new proof was obtained in [33, 34] using an algebraic-differential calculus (see also [10, 41]).”
- Mirror symmetry: from categories to curve counts (2015, result): “It was conjectured in [C˘al05, Conjecture 5.2] and proven in [ CRVdB12] (respectively, [Mar08, Ram08]) that this map respect the ‘calculus’ structure (respectively, the Mukai pairing).”
- 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”
- Derived categories of Gushel–Mukai varieties (2016, background): “ve variety, a more down-to-earth definition can be found in [24]. If A= Db(X), we write HH•(X) for HH•(A). There is the following version of the HKR isomorphism for Hochschild cohomology. Theorem 5.4 ([37]). Let Xbe a smooth projective variety. Then for all ithere is an isomorphism of vector spaces H”
- Dirichlet Branes and Mirror Symmetry (2009, background): “For some progress on this question see [348, 81, 82], as well as more recent progress in [80].”