## Algebraic & Geometric Topology

### Complete intersections and mod $p$ cochains

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 13, Number 1 (2013), 61-114.

Dates
Revised: 14 August 2012
Accepted: 14 August 2012
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715492

Digital Object Identifier
doi:10.2140/agt.2013.13.61

Mathematical Reviews number (MathSciNet)
MR3031637

Zentralblatt MATH identifier
1261.13007

#### Citation

Benson, David J; Greenlees, John P C; Shamir, Shoham. Complete intersections and mod $p$ cochains. Algebr. Geom. Topol. 13 (2013), no. 1, 61--114. doi:10.2140/agt.2013.13.61. https://projecteuclid.org/euclid.agt/1513715492

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