Volume 13, issue 1 (2013)

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Complete intersections and mod $p$ cochains

David J Benson, John P C Greenlees and Shoham Shamir

Algebraic & Geometric Topology 13 (2013) 61–114

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 p 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.

complete intersection, commutative ring spectrum, derived category, group cohomology, mod $p$ cochains
Mathematical Subject Classification 2010
Primary: 13C40, 55P43, 13D99, 20J06, 55N99
Secondary: 14M10, 55P42, 55U35, 20J05
Received: 15 April 2011
Revised: 14 August 2012
Accepted: 14 August 2012
Published: 6 February 2013
David J Benson
Department of Mathematics
University of Aberdeen
Meston Building
Aberdeen AB24 3UE
John P C Greenlees
School of Mathematics and Statistics
University of Sheffield
Hicks Building
Sheffield S3 7RH
Shoham Shamir
Department of Mathematics
University of Bergen
5008 Bergen