共查询到20条相似文献,搜索用时 15 毫秒
2.
Ross E. Staffeldt 《K-Theory》1989,2(4):511-532
In this work we present proofs of basic theorems in Quillen's algebraic K-theory of exact categories. The proofs given here are simpler and more straight-forward than the originals. 相似文献
3.
4.
Kazuhisa Shimakawa 《K-Theory》1991,5(4):355-371
We study the Mackey structure of the G-spectrum K
G
C associated to a monoidal G-category C. It is proved that the coefficient system of K
G
C coincides, as a (graded) Mackey functor, with the system of equivariant K-groups in the sense of Fröhlich and Wall. It is also shown that for any exact category U, there exists a G-spectrum Q
G
U representing the equivariant K-theory of U in the sense of Dress and Kuku, and that Q
G
U is naturally G-homotopy equivalent to K
G
IsoU if every short exact sequence in U splits. 相似文献
5.
Waldhausen defined the algebraic K-theory of categories with cofibrations and weak equivalences. In many examples, these categories arise as full subcategories of model categories in the sense of Quillen. We use parts of the additional structure coming from model categories to compare the algebraic K-theory of different categories. The main tool for this is a generalization of Waldhausen's Approximation Theorem. 相似文献
6.
We investigate the homotopy type of
(M)/TOP(M), where M is a compact manifold, TOP(M) is the simplicial group of homeomorphisms of M which restrict to the identity on ∂M, and
is the simplicial group of block homeomorphisms of M which restrict to the identity on ∂M. In the so-called topological concordance stable range of M, we obtain an expression in terms of the topological Whitehead spectrum of M. If M is smooth, we also investigate the homotopy type of
(M)/DIFF(M); in the smooth concordance stable range of M, it has an expression in terms of the smooth Whitehead spectrum of M. 相似文献
7.
Yongjin Song 《K-Theory》1991,5(6):485-501
We define the Volodin hermitian algebraic K-theory for a (discrete) ring with an involution and show that it is isomorphic to Karoubi's hermitian algebraic K-theory. We also construct the Volodin model
X(R
*) of hermitian algebraic K-theory for a simplicial ring R
* and show that it is a homotopy fiber of the map B
Ô(R
*)B
Ô(R
*)+. We also prove the general linear version of this result, which has been claimed in the existing literature, but whose proof was overlooked. 相似文献
8.
Boris Goldfarb 《Topology and its Applications》2004,140(2-3):267-294
New compactifications of symmetric spaces of noncompact type X are constructed using the asymptotic geometry of the Borel–Serre enlargement. The controlled K-theory associated to these compactifications is used to prove the integral Novikov conjecture for arithmetic groups. 相似文献
9.
Andrew J. Nicas 《K-Theory》1987,1(5):437-456
Deligne defined the notion of a mixed Hodge structure (MHS) and proved that every quasiprojective variety over has a natural MHS on its cohomology. This paper establishes similar results for cyclic homology and the algebraic K-theory of simply connected quasi-projective varieties over . In the nonsimply connected case, an MHS is established on certain quotient groups of algebraic K-theory.Supported by a NSERC University Research Fellowship and operating grant. 相似文献
10.
Jeff Kiralis 《K-Theory》1996,10(2):135-174
A non-Abelian version of algebraic K-theory, based on automorphism of free products rather than automorphisms of free modules, is considered and is related to pseudo-isotopies of 3-manifolds.Sometime after writing this paper I learned that some of the algebraic results in it were first proved by Gersten in [13]. Specifically each of Theorems 3.1, 3.2 and 5.1 in the special case when is the trivial group, and Theorem 3.3 and its corollaries are all results of Gersten. I have left the paper as it is for the sake of completeness and since the approach here often differs considerably from Gersten's. 相似文献
11.
We give a computation of the K-groups of Grassmannians and flag varieties over an arbitrary Noetherian base scheme. We also compute the K-groups of forms of Grassmannians and flag varieties associated to a sheaf of Azumaya algebras. One ingredient in the computation is the extension of the Bott theorem on the cohomology of line bundles on the flag variety (over Q) to a K
0-Bott theorem valid over arbitrary Noetherian base schemes.Partially supported by the NSF. 相似文献
12.
Henri Gillet 《K-Theory》1987,1(4):405-415
Another proof that the product structure on K-theory may be used to define the product structure on the Chow ring of a smooth variety over a field is presented. The virtue of this proof is that it is essentially a formal argument using natural properties of Quillen's spectral sequence, the K-theory product, cycle classes, and the classical intersection product. 相似文献
13.
Jerry M. Lodder 《K-Theory》1996,10(2):175-196
We establish a rational isomorphism between certain relative versions of Hermitian K-theory and the dihedral homology of simplicial Hermitian rings. This is the dihedral analogue of Goodwillie's result for cyclic homology and algebraic K-theory. In particular, we describe involutions on (negative) cyclic homology and the K-theory of simplicial rings. We show that Goodwillie's map from K-theory to negative cyclic homology can be chosen to preserve involutions. By work of Burghelea and Fiedorowicz the invariants of the involution on K-theory can be identified with symmetric Hermitian K-theory. Finally, we show how the author's chain complex defining dihedral homology can be extended to the left to capture the invariants of the involution on negative cyclic homology.Supported by New Mexico State University, grant No. RC90-051. 相似文献
14.
We decompose the K-theory space of a Waldhausen category in terms of its Dwyer–Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria appearing in the literature. We show that under mild hypotheses, a weakly exact functor that induces an equivalence of homotopy categories induces an equivalence of K-theory spectra. 相似文献
15.
Ernesto Vallejo 《K-Theory》1991,4(5):411-443
We adapt here the results of the author concerning polynomial operations on the 0th stable cohomotopy to the case of the 0th complex K-theory and consider polynomial operations : Kh, where h is a ring-valued contravariant functor, defined on finite CW-complexes, satisfying some properties. We construct a family of generating operations for the ring Pol(K,h) of all polynomial operations : Kh and doing so, we describe the additive structure of this ring in terms of the h(BU(n)'s. As an illustration of how polynomiality could be used to study operations in the setting of algebraic K-theory, we consider, from our point of view, the well known situation operations : KK on complex K-theory. 相似文献
16.
Reza Akhtar 《K-Theory》2004,32(3):269-291
Let k be a field and X a smooth projective variety of dimension d over k. Generalizing a construction of Kato and Somekawa, we define a Milnor-type group
which is isomorphic to the ordinary Milnor
We prove that
is isomorphic to both the higher Chow group CHd+s (X,s) and the Zariski cohomology group
相似文献
17.
A. Daele 《K-Theory》1992,6(5):465-485
LetA be a real or complex Banach algebra and assume that is an action of a finite groupG onA by means of continuous automorphisms. To such a finite covariant system (A, G, ), we associate an Abelian groupK(A, G, ). We obtain some classical exact sequences for an algebraA and a closed invariant idealI. We also compute the group in a few important special cases. Doing so, we relate our new invariant to the classicalK
0 andK
1 of a Banach algebra and to theK-theory of 2-graded Banach algebras. Finally, we obtain a result that gives a close relationship of our groupK(A, G, ) with theK-theory of the crossed productA
G. In particular, we prove a six-term exact sequence involving our groupK(A, G, ) and theK-groups ofA
G. In this way, we hope to contribute to the well-known problem of finding theK-theory of the crossed productA
G in the case of an action of a finite group. 相似文献
18.
19.
Daniel R. Grayson 《K-Theory》1989,3(3):247-260
We construct operations on higher algebraic K-groups induced by operations such as exterior power on any suitable exact category, without appeal to the plus-construction of Quillen.Dedicated to Alexander Grothendieck on his sixtieth birthdaySupported by NSF grants DMS 85-04692, 86-01980. 相似文献
20.
Thomas Hüttemann 《Journal of Pure and Applied Algebra》2002,170(2-3)
In the spirit of “The Fundamental Theorem for the algebraic K-theory of spaces: I” (J. Pure Appl. Algebra 160 (2001) 21–52) we introduce a category of sheaves of topological spaces on n-dimensional projective space and present a calculation of its K-theory, a “non-linear” analogue of Quillen's isomorphism Ki(PRn)0nKi(R). 相似文献