Reduction of derived Hochschild functors over commutative algebras and schemes |
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Authors: | Luchezar L. Avramov Srikanth B. Iyengar |
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Affiliation: | a Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA b Department of Mathematics, Purdue University, W. Lafayette, IN 47907, USA c Chennai Mathematical Institute, Siruseri 603103, India |
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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 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 of noetherian schemes, with f!OY in place of D. |
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Keywords: | primary, 13D03, 14B25 secondary, 14M05, 16E40 |
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