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arXiv · 1001.0902

Homological dimensions of ring spectra

Mark Hovey·Keir Lockridge
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Abstract

We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is the global dimension of real K-theory KO and its connective version ko at the prime 2. We show that the global dimension of KO is 1, 2, or 3, and the global dimension of ko is 4 or 5.

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Mark Hovey, Keir Lockridge. 2010-01-06. Homological dimensions of ring spectra. https://arxiv.org/abs/1001.0902

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