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Complete intersections
and mod $p$ cochains
David J Benson, John P C Greenlees and Shoham Shamir |
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Algebraic & Geometric Topology 13 (2013) 61–114
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Abstract |
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We give homotopy invariant definitions corresponding to three well-known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod cochains on a space, showing that suitable versions of the second and third are equivalent and that the first is stronger. We are particularly interested in classifying spaces of groups, and we give a number of examples. The case of rational homotopy theory is treated in [J. Pure Appl. Algebra 217 (2013) 636–663], and there are some interesting contrasts. |
Keywords
complete intersection, commutative ring spectrum, derived
category, group cohomology, mod $p$ cochains
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Mathematical Subject Classification 2010
Primary: 13C40, 55P43, 13D99, 20J06, 55N99
Secondary: 14M10, 55P42, 55U35, 20J05
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References |
Publication
Received: 15 April 2011
Revised: 14 August 2012
Accepted: 14 August 2012
Published: 6 February 2013
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Authors |
| David J Benson | |
| Department of Mathematics University of Aberdeen Meston Building Aberdeen AB24 3UE UK |
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| http://homepages.abdn.ac.uk/mth192/pages/html/index.html | |
| John P C Greenlees | |
| School of Mathematics and
Statistics University of Sheffield Hicks Building Sheffield S3 7RH UK |
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| http://greenlees.staff.shef.ac.uk | |
| Shoham Shamir | |
| Department of Mathematics University of Bergen 5008 Bergen Norway |
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