Continuous Morava K-Theory and the Geometry of the In-Adic Tower.
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Correction to the paper “Classical motivic polylogarithm according to Beilinson and Deligne”.
Crystalline conjecture via -theory
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.
Cyclic Cohomology, Supersymmetry and KMS States The KMS States as Generalized Elliptic Operators
Das Adams-Riemann-Roch-Theorem in der höheren äquivarianten K-Theorie.
Decomposition of the Grothendieck group of stable categories of finite groups.
Decompositions of the category of noncommutative sets and Hochschild and cyclic homology
In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.
Densities of 4-ranks of K₂(𝒪)
Descent, motives and K-theory.
Differential Equations associated to Families of Algebraic Cycles
We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.
Differentials in the homological homotopy fixed point spectral sequence.
Dilogarithm, grassmannian complex and scissors congruence groups of algebraic polyhedra
Dimension theory and nonstable -theory for net groups
Dirichlet motives via modular curves
Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere.