Excision in algebraic obstruction theory
نویسندگان
چکیده
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 کاملThe Obstruction to Excision in K-theory and in Cyclic Homology
Let f : A → B be a ring homomorphism of not necessarily unital rings and I ⊳ A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K∗(A : I) → K∗(B : f(I)) to be an isomorphism; it is measured by the birelative groups K∗(A,B : I). Similarly the groups HN∗(A,B : I) measure the obstruction to ex...
متن کاملObstruction Theory in Model
Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obst...
متن کاملObstruction Theory in Model Categories
Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obst...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2012
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2012.02.008