منابع مشابه
Excision in Algebraic K-theory (after Suslin)
(1) K1(A)→ K1(A/I)→ K0(I)→ K0(A)→ K0(A/I)→ K−1(I)→ · · · . Soon it was realized that in general one cannot expect this sequence to be continued on the left. This problem, known as excision in algebraic K-theory, was solved in [4] in characteristic zero and in [3] in general. In [1, Thm. 3.1] and in [2] a pro-version of excision is deduced. Theorem (Suslin–Wodzicki, Suslin) If TorIoZ i (Z,Z) = 0...
متن کاملExcision in algebraic K-theory and Karoubi's conjecture.
We prove that the property of excision in algebraic K-theory is for a Q-algebra A equivalent to the H-unitality of the latter. Our excision theorem, in particular, implies Karoubi's conjecture on the equality of algebraic and topological K-theory groups of stable C*-algebras. It also allows us to identify the algebraic K-theory of the symbol map in the theory of pseudodifferential operators.
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....
متن کاملAlgebraic 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....
متن کاملDeloopings in Algebraic K-theory
A crucial observation in Quillen’s definition of higher algebraic K-theory was that the right way to proceed is to define the higer K-groups as the homotopy groups of a space ([21]). Quillen gave two different space level models, one via the plus construction and the other via the Q-construction. The Q construction version allowed Quillen to prove a number of important formal properties of the ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1971
ISSN: 0022-4049
DOI: 10.1016/0022-4049(71)90020-x