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1.
Let X be a smooth complex variety, and let F be its function field. We prove that (after localizing at the prime 2) the K-groups of F are divisible above the dimension of X, and that the K-groups of X are divisible-by-finite. We also describe the torsion in the K-groups of F and X.  相似文献   

2.
We investigate the Chow groups of zero cycles of products of curves over a p-adic field by means of the Milnor K-groups of their Jacobians as introduced by Somekawa. We prove some finiteness results for CH 0(X)/m for X a product of curves over a p-adic field.  相似文献   

3.
It is proved that under certain conditions the group K n (X) of a smooth projective variety X over a field F is a natural direct summand of K n (A) for some separable F-algebra A. As an application we study the K-groups of toric models and toric varieties. A presentation in terms of generators and relations of the groupK 0(T) for an algebraic torus T is given.  相似文献   

4.
Aderemi Kuku 《K-Theory》2005,36(1-2):51-58
In this paper, we prove that if R is the ring of integers in a number field F, A any R-order in a semisimple F-algebra, then K2n(A), G2n(A) are finite groups for all positive integers n. Hence, even dimensional higher K- and G-groups of integral grouprings of finite groups are finite. We also show that in odd dimensions, SKn of integral and p-adic integral grouprings of finite p-groups are also finite p-groups (Received: August 2005)  相似文献   

5.
In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2.  相似文献   

6.
Matt Kerr 《K-Theory》2003,29(3):175-210
The classical Abel–Jacobi map is used to geometrically motivate the construction of regulator maps from Milnor K-groups K n M (C(X)) to Deligne cohomology. These maps are given in terms of some new, explicit (n – 1)-currents, higher residues of which are defined and related to polylogarithms. We study their behavior in families X s and prove a rigidity result for the regulator image of the Tame kernel, which leads to a vanishing theorem for very general complete intersections.  相似文献   

7.
Holger Reich 《K-Theory》2001,24(4):303-326
We construct a real valued dimension for arbitrary modules over the algebra of operators affiliated to a finite von Neumann algebra. Moreover we determine the algebraic K 0- and K 1-group and the L-groups of such an algebra. Mathematics Subject Classifications (2000): Primary 18F25; Secondary 46L10.  相似文献   

8.
We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.  相似文献   

9.
We are concerned with infinite-dimensional locally soluble linear groups of infinite central dimension that are not soluble A3-groups and all of whose proper subgroups, which are not soluble A3-groups, have finite central dimension. The structure of groups in this class is described. The case of infinite-dimensional locally nilpotent linear groups satisfying the specified conditions is treated separately. A similar problem is solved for infinite-dimensional locally soluble linear groups of infinite fundamental dimension that are not soluble A3-groups and all of whose proper subgroups, which are not soluble A3-groups, have finite fundamental dimension. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 548–559, September–October, 2007.  相似文献   

10.
Ruy Exel 《K-Theory》1993,7(3):285-308
GivenC*-algebrasA andB and an imprimitivityA-B-bimoduleX, we construct an explicit isomorphismX *:K i (A)K i (B), whereK i denotes the complexK-theory functors fori=0, 1. Our techniques do not require separability nor the existence of countable approximate identities. We thus extend to generalC*-algebras the result of Brown, Green, and Rieffel according to which, strongly Morita equivalentC*-algebras have isomorphicK-groups. The method employed includes a study of Fredholm operators on Hilbert modules.On leave from the University of São Paulo, Brazil.  相似文献   

11.
We consider the ring Kr(F/D), where D is a subring of a field F, that is the intersection of the trivial extensions to F(X) of the valuation rings of the Zariski–Riemann space consisting of all valuation rings of the extension F/D and investigate the ideal structure of Kr(F/D) in the case where D is an affine algebra over a subfield K of F and the extension F/K has countably infinite transcendence degree, by using the topological structure of the Zariski–Riemann space. We show that for any pair of nonnegative integers d and h, there are infinitely many prime ideals of dimension d and height h that are minimal over any proper nonzero finitely generated ideal of Kr(F/D).  相似文献   

12.
Abstract. Let K be an algebraic number field and F(X, Y ) be an absolutelyirreducible polynomial of K[X, Y ] such that the curve defined by the equation F(X, Y ) = 0 is of genus 0 with at least threeinfinite valuations. In this paper we establish explicit upper bounds forthe size of integral solutions to the equation F(X, Y ) = 0 defined over K,improving significantly earlier estimates.  相似文献   

13.
Kei Hagihara 《K-Theory》2003,29(2):75-99
In this paper we develop a K-theory of log schemes by using vector bundles on the Ket site. Then, for a wide class of log varieties, we describe the structure of their K-groups in terms of the usual algebraic K-groups.  相似文献   

14.
LetK be a field such that all Sylow subgroups of its absolute Galois groupG Kare infinite. LetX be a smooth variety overK with function fieldF andY→X the normalisation in a finite, separable extensionE/vbF. We show: If there is a closed pointx∈X which does not split completely inY→X, then the set of these points is Zariski dense inX.  相似文献   

15.
A space X is called Moscow if the closure of any open set is the union of some family of G -subsets of X. It is established that if a topological ring K of non-measurable cardinality is a Moscow space, then the operations in K can be continuously extended to the Hewitt–Nachbin completion K of K turning K into a topological ring as well. A similar fact is established for linear topological spaces. If F is a topological field such that the cardinality of F is non-measurable and the space F is Moscow, then the space F is submetrizable and the space F is hereditarily Hewitt–Nachbin complete. In particular, F=F. We also show the effect of homogeneity of the Hewitt–Nachbin completion on the commutativity of the Hewitt–Nachbin completion with the product operation.  相似文献   

16.
Max Karoubi 《K-Theory》2001,24(2):109-114
We prove the Lichtenbaum–Quillen conjecture in the topological context: in other words, real K-theory can be deduced from complex K-theory via the usual descent spectral sequence. More precise results are proved, however, and new applications are stated. The main ingredients in the proof are Atiyah's KR-theory and the definition of higher K-groups via Clifford algebras.  相似文献   

17.
Mark E. Walker 《K-Theory》2000,21(2):101-140
We establish the existence of Adams operations on the members of a filtration of K-theory which is defined using products of projective lines. We also show that this filtration induces the gamma filtration on the rational K-groups of a smooth variety over a field of characteristic zero.  相似文献   

18.
We define a multifunction F: XY to be upper (lower) D*-supercontinuous if F +(V) (F (V)) is d*-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) D*-supercontinuous multifunctions.   相似文献   

19.
Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.  相似文献   

20.
It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T 0-space X is a subspace of the quasi-proximity space induced by the Samuel bicompactification of X. The result is then used to establish that the locally finite covering quasi-uniformity defined on the category Top 0 of topological T 0-spaces and continuous maps is not lower K-true (in the sense of Brümmer). It is also shown that a functorial quasi-uniformity F on Top 0 is upper K-true if and only if FX is bicomplete whenever X is sober.  相似文献   

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