A reciprocity law for K2-traces.
A Riemann-Roch-Hirzebruch formula for traces of differential operators
Let be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators on a formal neighbourhood of a...
A splitting principle and the algebraic K-theory of some homogeneous varieties
A stably free nonfree module and its relevance for homotopy classification, case .
A Thom isomorphism for infinite rank Euclidean bundles.
A twisted class number formula and Gross's special units over an imaginary quadratic field
Let be a finite abelian extension of number fields with imaginary quadratic. Let be the ring of integers of and a rational integer. We construct a submodule in the higher odd-degree algebraic -groups of using corresponding Gross’s special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher “twisted” class number of , which is the cardinal of the finite algebraic -group .
Abelian local p-class field theory.
Actions and automorphisms of crossed modules
Algebraic cycles and the classical groups II: quaternionic cycles.
Algebraic -theory and etale cohomology
Algebraic -theory and sums-of-squares formulas.
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 and Quadratic Forms.
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...
Algebraic properties of decorated splitting obstruction groups
In questo articolo si riassumono le definizioni e le principali proprietà dei gruppi di ostruzione con decorazione di tipo LS e LP. Si stabiliscono nuove relazioni fra questi gruppi e si descrivono le proprietà delle mappe naturali fra differenti gruppi con decorazione. Si costruiscono varie successioni spettrali, contenenti questi gruppi con decorazione, e si studiano la loro connessione con le successioni spettrali in -teoria per certe estensioni quadratiche di antistrutture. Infine, si introduce...
An additive version of higher Chow groups
An application of Burnside rings in elementary finite group theory.
An example of a subalgebra of on the unit disk whose stable rank is not finite
We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
An inverse -theory functor.