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