Related papers: Torsion algebraic cycles and complex cobordism

For every even number $n$, and every $n$-dimensional smooth hypersurface of $\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its $\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore, we determine the…

In this paper we focus on the set-open topologies on the group $\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group operations, product and inverse function. As a consequence, we…

We give a formalism of arithmetic mixed sheaves including the case of arithmetic mixed Hodge structures, and show the nonvanishing of certain higher extension groups, and also the nontriviality of the second Abel-Jacobi map for zero cycles…

We explore the special structure of the top-dimensional homology of any compact triangulable space $X$ of dimension $d$. Since there are no $(d+1)$-dimensional cells, the top homology equals the top cycles and is thus a free abelian group.…

A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in…

Described the algebraic structure on the space of homotopy classes of cycles with marked topological flags of disks. This space is a non-commutative monoid, with an Abelian quotient corresponding to the group of singular homologies…

Let $X$ be a smooth affine algebraic variety over the field of complex numbers which is contractible. Then every algebraic $G$-torsor on $X$ is algebraically trivial if $G$ is a semi-simple algebraic group. We also show that if $X$ is a…

Based on the ideas of Cuntz and Quillen, we give a simple construction of cyclic homology of unital algebras in terms of the noncommutative de Rham complex and a certain differential similar to the equivariant de Rham differential. We…

To study the set of torsion classes of a finite dimensional basic algebra, we use a decomposition, called sign-decomposition, parametrized by elements of $\{\pm1\}^n$ where $n$ is the number of simple modules. If $A$ is an algebra with…

Let \(X\subset \mathbb{P}^{n+1}\) be a smooth cubic hypersurface, and let \(F(X)\) be the variety of lines on \(X\). We prove the surjectivity of the cylinder maps on the Chow groups of \(F(X)\) and \(X\) if \(X\) contains a one-cycle of…

We show that the extended noncommutative de Rham complex of a cofibrant resolution, when completed at a certain Hodge filtration, is (reduced) quasi-isomorphic to the periodic cyclic complex, while each of its filtration piece is…

A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic…

The goal of this article is to try understand where Hodge cycles on a singular complex projective variety X come from. As a first step we consider Hodge cycles on the maximal pure quotient $H^{2p}(X)/W_{2p-1}$, and introduce a class of…

We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological cyclic homology at a prime $p$ of the group algebra of a discrete group $G$ with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite group, we…

We study the injectivity property of certain actions of higher Chow groups on refined unramified cohomology. As an application for every $p\geq1$ and for each $d\geq p+4$ and $n\geq2,$ we establish the first examples of smooth complex…

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected base $S$, with everything defined over $\overline{\mathbb{Q}}$. Denote by $\mathbb{V} = R^{2i} f_{*} \mathbb{Z}(i)$ the associated integral…

Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes…

The purpose of this article is to prove that the category of cocommutative Hopf $K$-algebras, over a field $K$ of characteristic zero, is a semi-abelian category. Moreover, we show that this category is action representable, and that it…

We write down a new "logarithmic" quasicoherent category $\operatorname{Qcoh}_{log}(U, X, D)$ attached to a smooth open algebraic variety $U$ with toroidal compactification $X$ and boundary divisor $D$. This is a (large) symmetric monoidal…

We show that the octonions are a twisting of the group algebra of Z_2 x Z_2 x Z_2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-cocycle. We consider general quasi-associative algebras of this…