First steps in brave new commutative algebra
J.P.C.Greenlees
TL;DR
This paper provides an expository overview of completion and local cohomology in brave new commutative algebra, highlighting their applications to completion theorems and dualities in equivariant topology, with discussions on Morita theory and Gorenstein ring spectra.
Contribution
It offers a comprehensive exposition connecting advanced algebraic concepts with topological applications, including new insights into Gorenstein ring spectra and Morita theory in the context of brave new algebra.
Findings
Clarifies the role of local cohomology in equivariant topology
Explores Morita theory in the setting of ring spectra
Discusses Gorenstein properties of ring spectra
Abstract
This is an expository account of completion and local cohomology in brave new commutative algebra, especially as it applies to completion theorems and their duals in equivariant topology. The first part is fairly direct, but the second considers Morita theory and Gorenstein ring spectra. This draws on work of the author with Benson, Dwyer, Iyengar and May, amongst others.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra