### Abstract

Original language | English |
---|---|

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 |

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### Keywords

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

### Cite this

*Algebraic & Geometric Topology*,

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

**Complete intersections and mod p cochains.** / Benson, David J.; Greenlees, John P. C.; Shamir, Shoham.

Research output: Contribution to journal › Article

*Algebraic & Geometric Topology*, vol. 13, no. 1, pp. 61-114. https://doi.org/10.2140/agt.2013.13.61

}

TY - JOUR

T1 - Complete intersections and mod p cochains

AU - Benson, David J.

AU - Greenlees, John P. C.

AU - Shamir, Shoham

PY - 2013/2/6

Y1 - 2013/2/6

N2 - 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.

AB - 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.

KW - complete intersection

KW - commutative ring spectrum

KW - derived category

KW - group cohomology

KW - mod p cochains

U2 - 10.2140/agt.2013.13.61

DO - 10.2140/agt.2013.13.61

M3 - Article

VL - 13

SP - 61

EP - 114

JO - Algebraic & Geometric Topology

JF - Algebraic & Geometric Topology

SN - 1472-2747

IS - 1

ER -