A bound for the torsion in the -theory of algebraic integers.
A counterexample to a conjecture of Barr.
A Homotopy Theoretical Derivation of Q Map (K, -).
A note on product structures on Hochschild homology of schemes
We extend the definition of Hochschild and cyclic homologies of a scheme over a commutative ring k to define the Hochschild homologies HH⁎(X/S) and cyclic homologies HC⁎(X/S) of a scheme X with respect to an arbitrary base scheme S. Our main purpose is to study product structures on the Hochschild homology groups HH⁎(X/S). In particular, we show that carries the structure of a graded algebra.
Abelian local p-class field theory.
Actions and automorphisms of crossed modules
Algebraic -theory of Fredholm modules and -theory.
Algebraic -theory of the first Morava -theory
For a prime , we compute the algebraic -theory modulo and of the mod Adams summand, using topological cyclic homology. On the way, we evaluate its modulo and topological Hochschild homology. Using a localization sequence, we also compute the -theory modulo and of the first Morava -theory.
Algebraic K-theory of rings from a topological viewpoint.
Because of its strong interaction with almost every part of pure mathematics, algebraic K-theory has had a spectacular development since its origin in the late fifties. The objective of this paper is to provide the basic definitions of the algebraic K-theory of rings and an overview of the main classical theorems. Since the algebraic K-groups of a ring R are the homotopy groups of a topological space associated with the general linear group over R, it is obvious that many general results follow...
An additive version of higher Chow groups
An inverse -theory functor.
Chow groups with coefficients.
Coherence of the double involution on -autonomous categories.
Cohomologie des algèbres de Lie croisées et -théorie de Milnor additive
Dans cet article, nous définissons des modules de (co)-homologie , , , , où et sont des algèbres de Lie munies d’une structure supplémentaire (algèbres de Lie croisées), qui satisfont les propriétés usuelles des foncteurs cohomologiques. Si est une -algèbre, nous utilisons ces modules d’homologie pour comparer le groupe d’homologie cyclique avec un analogue additif du groupe de -théorie de Milnor .
Cohomologies bivariantes de type cyclique
In the article we propose a construction of bivariant cohomology of a couple of chain complexes with periodicities. In this way we obtain definitions of bivariant dihedral and bivariant reflective cohomology of an algebra . Bivariant cyclic and quaternionic cohomologies appear as particular cases of this construction. The case of invertible in the ground ring is studied particulary.Dans cet article nous proposons une définition de la cohomologie bivariante pour une paire de complexes de chaînes...
Cohomology of some graded differential algebras
We study cohomology algebras of graded differential algebras which are models for Hochschild homology of some classes of topological spaces (e.g. homogeneous spaces of compact Lie groups). Explicit formulae are obtained. Some applications to cyclic homology are given.
Cubic structures and ideal class groups
Curvature, tangentiality, and controlled topology.
Cyclic cohomology of certain nuclear Fréchet algebras and DF algebras
We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain -algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ϕ: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H...
Cyclic cohomology of (extended) Hopf algebras
We review recent progress in the study of cyclic cohomology of Hopf algebras, extended Hopf algebras, invariant cyclic homology, and Hopf-cyclic homology with coefficients, starting with the pioneering work of Connes-Moscovici.