### 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.

Original language | English |
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Pages (from-to) | 61-114 |

Number of pages | 54 |

Journal | Algebraic & Geometric Topology |

Volume | 13 |

Issue number | 1 |

DOIs | |

Publication status | Published - 6 Feb 2013 |

### Keywords

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

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## Cite this

Benson, D. J., Greenlees, J. P. C., & Shamir, S. (2013). Complete intersections and mod p cochains.

*Algebraic & Geometric Topology*,*13*(1), 61-114. https://doi.org/10.2140/agt.2013.13.61