Algebraic & Geometric Topology

Complete intersections and mod $p$ cochains

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

Full-text: Open access

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
Received: 15 April 2011
Revised: 14 August 2012
Accepted: 14 August 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Subjects
Primary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 13D99: None of the above, but in this section 20J06: Cohomology of groups 55N99: None of the above, but in this section
Secondary: 14M10: Complete intersections [See also 13C40] 55P42: Stable homotopy theory, spectra 55U35: Abstract and axiomatic homotopy theory 20J05: Homological methods in group theory

Keywords
complete intersection commutative ring spectrum derived category group cohomology mod $p$ cochains

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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