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We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
A kind of motivic stable homotopy theory of algebras is developed. Explicit fibrant replacements for the S^1-spectrum and (S^1,\G)-bispectrum of an algebra are constructed. As an application, unstable...
Abstract: In this paper, we use $\mathcal D$-split sequences and derived equivalences to provide formulas for calculation of higher algebraic $K$-groups (or mod-$p$ $K$-groups) of certain matrix subri...
Let A be a not necessarily commutative monoid with zero such that projective A-acts are free. This paper shows that the algebraic K-groups of A can be defined using the +-construction and the Q-constr...
The paper revisits concretely the algebraic K -theory in the light of the global program of Langlands by taking into account the new algebraic interpretation of homotopy viewed as deformation(s) of Ga...

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