Duality in algebra and topology |
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| Authors: | W.G. Dwyer J.P.C. Greenlees S. Iyengar |
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| Affiliation: | aDepartment of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA;bDepartment of Pure Mathematics, Hicks Building, Sheffield S3 7RH, UK;cDepartment of Mathematics, University of Nebraska, Lincoln, NE 68588, USA |
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| Abstract: | We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson–Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross–Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon. |
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| Keywords: | Duality Poincaré duality Gorenstein Benson– Carlson duality Local cohomology Ring spectra -algebras Cellular Small Proxy-small Matlis duality Matlis lifts Brown– Comenetz duality Morita theory Derived category |
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