Related papers: Totaro's Question on Zero-Cycles on Torsors

Let $G$ be a smooth connected linear algebraic group and $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$ have a closed \'etale point of degree dividing $d$? This question is entirely…

Let $G$ be a smooth connected linear algebraic group over a field $k$, and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$ have a closed \'etale point of degree dividing $d$? We give an…

In a 2004 paper, Totaro asked whether a G-torsor X that has a zero-cycle of degree d > 0 will necessarily have a closed etale point of degree dividing d, where G is a connected algebraic group. This question is closely related to several…

Let $k$ be a perfect field of virtual cohomological dimension $\leq 2$. Let $G$ be a connected linear algebraic group over $k$ such that $G^{sc}$ satisfies a Hasse principle over $k$. Let $X$ be a principal homogeneous space under $G$ over…

By using the triangulated category of \'etale motives over a field $k$, for a smooth projective variety $X$ over $k$, we define the group $\text{CH}^\text{\'et}_0(X)$ as an \'etale analogue of 0-cycles. We study the properties of…

Following an idea of Totaro, we prove that the classical integral cycle class map from algebraic cycles to \'etale cohomology factors through a quotient of $\ell$-adic \'etale cobordism over an algebraically closed field of positive…

Let $k$ be a field of characteristic different from 2. Let $G$ be a simply connected or adjoint semisimple algebraic $k$-group which does not contain a simple factor of type $E_8$ and such that every exceptional simple factor of type other…

We show that the cycle map on a variety X, from algebraic cycles modulo algebraic equivalence to integer cohomology, lifts canonically to a topologically defined quotient of the complex cobordism ring of X. This more refined cycle map gives…

This is an essentially extended version of the preprint dated by August 2005 (this includes now the varieties of types F_4, E_6 and E_7). Let k be a field of characteristic not 2 and 3. Let G be an exceptional simple algebraic group of type…

We relate the torsion part of the Abel-Jacobi kernel in the Griffiths group of 1-cycles to a birational invariant analogous to the degree 4 unramified cohomology and an invariant associated to the generalized Hodge conjecture in degree…

For 0-cycles on a variety over a number field, we define an analogue of the classical descent set for rational points. This leads to, among other things, a definition of the \'etale-Brauer obstruction set for 0-cycles, which we show is…

Does every one-ended $CAT(0)$ group have semistable fundamental group at infinity? As we write, this is an open question. Let $G$ be such a group acting geometrically on the proper $CAT(0)$ space $X$. In this paper we show that in order to…

Let $R$ be a complete discrete valuation ring with fraction field $K$ and with algebraically closed residue field. Let $X$ be a faithfully flat $R$-scheme of finite type of relative dimension 1 and $G$ be any affine $K$-group scheme of…

Let $K$ be a periodic cell complex endowed with a covering $q:K\to G$ where $G$ is a finite quotient space of equivalence classes under translations acting on $K$. We assume $G$ is embedded in a space whose homotopy type is a $d$-torus for…

We study graded connected algebras over a field of characteristic zero and give an explicit formula for the cyclic homology of a tensor algebra. By means of a slightly new definition of David Anick's notion "strongly free" we are able to…

Let X be a smooth compactification of a connected linear algebraic group over a field k. The Chow group of degree nought zero-cycles on X is a torsion group. When k is a p-adic field, we show that the prime-to-p component of this group is…

This partly expository paper investigates versions of the Tate conjecture on the cycle map for varieties defined over finite fields with values in 'etale cohomology with Z_\ell-coefficients. The bulk of the paper is an exposition of a 1998…

The question of whether or not any zero torsion linear map on a non abelian real Lie algebra g is necessarily an extension of some CR-structure is considered and answered in the negative. Two examples are provided, one in the negative and…

Let G be the graph of a triangulated surface $\Sigma$ of genus $g\geq 2$. A cycle of G is splitting if it cuts $\Sigma$ into two components, neither of which is homeomorphic to a disk. A splitting cycle has type k if the corresponding…

Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or…