Tags: #homotopy/stable-homotopy #higher-algebra/K-theory

  • \(K^ \mathsf{Alg} ({\mathbb{S}})\) is of interest due to Waldhausen’s stable parameterized h-cobordism theorem.

    • How to understand it: look at Galois descent on \({\mathsf{K}}({\mathbf{Z}})\)
  • A first approximation: \({\mathsf{K}}^ \mathsf{Alg} (L_{K(n)} {\mathbb{S}})\), so localize with respect to Morava K-theory

  • Rognes extends Lichtenbaum-Quillen conjectures and develops a theory for Galois extensions of \({\mathbb{S}}{\hbox{-}}\)algebras

  • Redshift : algebraic K-theory increases chromatic complexity by one.

#web/quick-notes #homotopy/stable-homotopy #higher-algebra/K-theory