The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
We the study the algebraic K-theory of C *-algebras, forgetting the topology. The main results include a proof that commutative C*-algebras are K-regular in all degrees (that is, all theirNTKiand extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients.
We study the descent problem of modules over general extensions of noncommutative rings and give different interpretations of descent data. We consider in particular the case of Hopf–Galois extensions. When descent data exist, we classify them by non-Abelian cohomology sets and deduce a noncommutative version of Hilbert's Theorem 90.
We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.
It is proved that under certain conditions the group Kn(X) of a smooth projective variety X over a field F is a natural direct summand of Kn(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 groupK0(T) for an algebraic torus T is given.
Let $$\mathcal{U} $$ be an $$\mathcal{A} $$ -filtered category in the sense of Karoubi. This is the categorical analogue of an ideal $$\mathcal{A} $$ in a ring $$\mathcal{U} $$ . Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence $$\mathcal{A} $$ → $$\mathcal{U} $$ → $$\mathcal{U}{\text{/}}\mathcal{A} $$ . We present a...
We relate the ‘Hodge filtration’ of the cohomology of a complex algebraic variety X to the ‘Hodge decomposition’ of its cyclic homology. If X is smooth and projective, $$HC_n^{(i)} (X) $$ is the quotient of the Betti cohomology $$H^{2i - n} (X(\mathbb{C});\mathbb{C}) $$ by the $$(i + 1)^{st} $$ piece of the Hodge filtration.
Homology of bi-Grassmannian complex with rational coefficients is calculated. Some applications to the homological stabilization of linear groups are given.
For every Ore extension we construct a chain complex giving its Hochschild homology. As an application we compute the Hochschild and cyclic homology of an arbitrary multiparametric affine space and the Hochschild homology of the algebra of differential operators over this space, in the generic case.
We give a leafwise Lefschetz theorem in the localized equivariant K-theory of a compact foliated manifold. The method is a generalization of the one adopted by M.F. Atiyah and G. Segal in the nonfoliated case. The main tool is the equivariant version of the Connes–Skandalis longitudinal index theorem for foliations. As a byproduct, we obtain a generalization of the Heitsch–Lazarov measured Lefschetz...
We prove that for W2 $${\mathbb{F}}_q $$ the Witt vectors of length two over the finite field $$\mathbb{F}_q $$ , we have $${\text{K}}_{\text{3}} (W_2 (\mathbb{F}_{p^f } )) = (\mathbb{Z}/p^2 )^f \oplus \mathbb{Z}/(p^{2f} - 1) $$ in characteristic at least 5 and $${\text{K}}_{\text{3}} (W_2 (\mathbb{F}_{3^f } )) = (\mathbb{Z}/9)^{f - 1} \oplus (\mathbb{Z}/3)^2 \oplus \mathbb{Z}/(3^{2f}...
In this paper we shall study the indices of some leafwise elliptic operators on foliated bundles, by using some concretely constructed cyclic cocycles on the smooth foliation algebras. The key is a decomposition of the KK-classes associated to the operators. The group action analogue of this approach provides a bridge from the classical Atiyah-Singer index theorem to the higher Γ-index theorem of...
This paper deals with an index which is different in general from the topological index defined by Atiyah and Singer because we loosen the normalization property. The intrinsic relation of this new index with operations in K-theory is explained. It is also shown that if we change the normalization axiom, the corresponding index is well-defined and may be expressed in terms of the topological index.
We establish an equivariant generalization of the Novikov inequalities which allows us to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply these inequalities to study cohomology of the fixed points set of a symplectic torus action. We show that in this case our inequalities are perfect, i.e. they...
Let F be a field of characteristic ≠ 2 and φ an anisotropic quadratic form of dimension 8 such that φ ε I2F and the index of the Clifford algebra C(φ)is 8. In this paper, we give a complete characterization of quadratic forms ψ such that φ becomes isotropic over the function field F(φ)of the projective quadric defined by the equation φ=0. Mathematics Subject Classifications (1991): Primary 11E04,...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.