21:57
Tags: #homotopy/stable-homotopy #higher-algebra/K-theory
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\(K^ \mathsf{Alg} ({\mathbb{S}})\) is of interest due to Waldhausen’s stable parameterized h-cobordism theorem.
- How to understand it: look at Galois descent on \({\mathsf{K}}({\mathbf{Z}})\)
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A first approximation: \({\mathsf{K}}^ \mathsf{Alg} (L_{K(n)} {\mathbb{S}})\), so localize with respect to Morava K-theory
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Rognes extends Lichtenbaum-Quillen conjectures and develops a theory for Galois extensions of \({\mathbb{S}}{\hbox{-}}\)algebras
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Redshift : algebraic K-theory increases chromatic complexity by one.