Excision in algebraic $K$ -theory revisited

  title={Excision in algebraic \$K\$ -theory revisited},
  author={Georg Tamme},
  journal={Compositio Mathematica},
  pages={1801 - 1814}
  • Georg Tamme
  • Published 9 March 2017
  • Mathematics
  • Compositio Mathematica
By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic $K$ -theory. We give a new and direct proof of Suslin’s result based on an exact sequence of categories of perfect modules. In fact, we prove a more general descent result for a pullback square of ring spectra and any localizing invariant. Our descent theorem contains not only Suslin’s result, but also Nisnevich descent of algebraic $K$ -theory for affine schemes as special cases. Moreover, the… 

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