منابع مشابه
Topological K-theory of Algebraic K-theory Spectra
One of the central problems of algebraic K-theory is to compute the K-groups KX of a scheme X. Since these groups are, by definition, the homotopy groups of a spectrum KX, it makes sense to analyze the homotopy-type of the spectrum, rather than just the disembodied homotopy groups. In addition to facilitating the computation of the K-groups themselves, knowledge of the spectrum KX can be applie...
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Background. For X a smooth scheme over ~, K.t(X; 2g/{") is isomorphic to the usual rood(" topological K-theory of X as a complex manifold ([6]). In this case, Theorem 1 essentially answers a question of Fulton, [9], w 5. For many such X the mapp: Ko(X)~K~ot(X) cannot be a surjection, as non-trivial Hodge conditions on the Chern classes prevent some topological bundles from being stably algebrai...
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We prove a conjecture of Rognes that establishes a localization cofiber sequence of spectra K(Z) → K(ku) → K(KU) → ΣK(Z) for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage theorem identifying the K-theory of the Waldhausen category of Postnikov towers of modules over a connective A∞ ring spectrum R with the Quillen K-theo...
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We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive Ktheory of algebras over a fixed unital ground ring H, (A, B) 7→ kk∗(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel’s homotopy algebraic K-theory, KH....
متن کاملBivariant algebraic K-theory
We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive Ktheory of algebras over a fixed unital ground ring H, (A, B) 7→ kk∗(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel’s homotopy algebraic K-theory, KH....
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2002
ISSN: 0001-5962
DOI: 10.1007/bf02392794