Higher Algebraic K-Theory of Schemes and of Derived Categories

  title={Higher Algebraic K-Theory of Schemes and of Derived Categories},
  author={R. Thomason and Thomas Trobaugh},
In this paper we prove a localization theorem for the K-theory of commutative rings and of schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of the category of those perfect complexes on the scheme which are acyclic on the open subscheme. The localization theorem of Quillen [Q1] for K′- or G-theory is the main support of his many results on the G-theory of noetherian schemes. The previous lack of an adequate localization theorem for K-theory has obstructed… Expand
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