Reduction of derived Hochschild functors over commutative algebras and schemes
By L. Avramov, S. Iyengar, J. Lipman, S. Nayak. 2009
59 citations recorded by the source corpus.
Abstract We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of S-modules D, and natural reduction isomorphisms Ext S ⊗ K L S ∗ ( S | K ; M ⊗ K L N ) ≃ Ext S ∗ ( R Hom S ( M , D ) , N ) for all complexes of S-modules N and all complexes M of finite flat dimension over K whose homology H ( M ) is finitely generated over S; such isomorphisms determine D up to derived isomorphism. Using Grothendieck duality theory we establish analogous isomorphisms for any essentially finite-type flat map f : X → Y of noetherian schemes, with f ! O Y in place of D.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/283fa56c684494ad56f0720b2e115a4a8712d961
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In Geometry and Topology
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- Yukinobu Toda
- A. Ramadoss
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- James J. Zhang
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In Mathematical Physics
- Amnon Yekutieli
- Andrei Căldăraru
- Michel van den Bergh
- Yukinobu Toda
- A. Ramadoss
- Masaki Kashiwara
- Damien Calaque
- James J. Zhang
Citations in the corpus
- Derived Categories (2016, background): “It is worthwhile to mention that the correct proofs (both in [14] and [173]) rely on noncommutative DG rings and DG bimodules over them; and the squaring operation is replaced by the rectangle operation.”