#### Volume 13, issue 1 (2013)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Complete intersections and mod $p$ cochains

### David J Benson, John P C Greenlees and Shoham Shamir

Algebraic & Geometric Topology 13 (2013) 61–114
##### Abstract

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.

##### Keywords
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