Excision in Cyclic Homology and in Rational Algebraic K-theory

Wodzicki, Mariusz

doi:10.2307/1971518

Cited by 115 publications

(119 citation statements)

References 31 publications

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“…Thus if f is a cofibration then Bf is, because in each degree it is a finite direct sum of cofibrations. That B preserves fibrant objects is immediate from (16); that it commutes with finite pushouts is clear. To show that also weak equivalences are preserved, it suffices to show BM is weakly contractible if…”

Section: Mixed Complexesmentioning

confidence: 95%

Excision in Bivariant Periodic Cyclic Cohomology: A Categorical Approach

Cortiñas¹,

Valqui²

2003

K-Theory

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Section: Mixed Complexesmentioning

confidence: 95%

Excision in Bivariant Periodic Cyclic Cohomology: A Categorical Approach

Cortiñas¹,

Valqui²

2003

K-Theory

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“…The second statement in a) may be viewed as an excision theorem analogous to [164]. We refer to the recent proof [28] of Weibel's conjecture [162] on the vanishing of negative K-theory for an application of the theorem.…”

Section: 3mentioning

confidence: 99%

Differential graded categories

Tabuada¹

2015

University Lecture Series

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“…As A is unital, M ∞ A is excisive for both K Qtheory and HN Q (cf. [28]) and has the same K Q -and HN Q -groups as A. Moreover K Q * (ΓA) = HN Q * (ΓA) = 0.…”

Section: The Chern Character Is the Tautological Charactermentioning

confidence: 99%

“…Recall from [28] that C bar n (A) = 0 if n ≤ 0 and C bar n = A ⊗n if n ≥ 1, with boundary operator given by…”

Section: Proof Let C(a) = [Gl(a) Gl(a)]mentioning

confidence: 99%

The obstruction to excision in K-theory and in cyclic homology

Cortiñas

2005

Invent. math.

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Let $f:A \to B$ be a ring homomorphism of not necessarily unital rings and $I\triangleleft A$ 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 $K_*(A:I) \to K_*(B:f(I))$ to be an isomorphism; it is measured by the birelative groups $K_*(A,B:I)$. We show that these are rationally isomorphic to the corresponding birelative groups for cyclic homology up to a dimension shift. In the particular case when A and B are $\Q$-algebras we obtain an integral isomorphism.Comment: Final version to appear in Inventione

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Excision in Cyclic Homology and in Rational Algebraic K-theory

Cited by 115 publications

References 31 publications

Excision in Bivariant Periodic Cyclic Cohomology: A Categorical Approach

Excision in Bivariant Periodic Cyclic Cohomology: A Categorical Approach

Differential graded categories

The obstruction to excision in K-theory and in cyclic homology

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