Related papers: Zero-cycles on normal varieties

We study the 0-th stable A^1-homotopy sheaf of a smooth proper variety over a field k assumed to be infinite, perfect and to have characteristic unequal to 2. We provide an explicit description of this sheaf in terms of the theory of…

Let $X$ be a rationally connected algebraic variety, defined over a number field $k$. We find a relation between the arithmetic of rational points on $X$ and the arithmetic of zero-cycles. More precisely, we consider the following…

In this paper we extend the unramified class field theory for arithmetic surfaces of K. Kato and S. Saito to the relative case. Let X be a regular proper arithmetic surface and let Y be the support of divisor on X. Let CH_0(X,Y) denote the…

Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Th\'el\`ene, Sansuc, Kato and Saito in the 1980's. We prove that these conjectures are compatible with…

We show that the torsion in the group of indecomposable $(2,1)$-cycles on a smooth projective variety over an algebraically closed field is isomorphic to a twist of its Brauer group, away from the characteristic. In particular, this group…

Given a smooth projective variety $X$ over a field, consider the $\mathbb Q$-vector space $Z_0(X)$ of 0-cycles (i.e. formal finite $\mathbb Q$-linear combinations of the closed points of $X$) as a module over the algebra of finite…

Let $\bar{X}$ be a smooth quasi-projective $d$-dimensional variety over a field $k$ and let $D$ be an effective Cartier divisor on it. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the…

We use pro cdh-descent of $K$-theory to study the relationship between the zero cycles on a singular variety $X$ and those on its desingularisation $X'$. We prove many cases of a conjecture of S. Bloch and V. Srinivas, and relate the Chow…

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…

Colliot-Th{\'e}l{\`e}ne has determined the Chow group of zero-cycles on a Ch{\^a}telet surface X defined over a finite extension K of the field of p-adic numbers (p an odd prime) when X is split by an unramified extension of K. Using…

The aim of this article is to prove Bloch's conjecture, asserting that the group of rational equivalence classes of zero cycles of degree 0 is trivial for surfaces with geometric genus zero, for regular generalized Burniat type surfaces.…

Let $X$ be a surface with geometric genus and irregularity zero which is defined over a number field $K$. Let $\mathscr{X}$ denote a smooth spread of $X$ over the spectrum of a Zariski open subset in the spectrum of the ring of integers and…

We propose a "Bloch type" conjecture for surfaces: if the cup product map in coherent cohomology is zero, then all intersections of homologically trivial divisors should be zero in the Chow group of zero-cycles. We prove this conjecture for…

In this paper we study the group $A_0(X)$ of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety $X$. To do this we translate rational equivalence of 0-cycles on a projective variety…

For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow…

Auel-Bigazzi-B\"ohning-Graf von Bothmer proved that if a proper smooth variety $X$ over a field $k$ of characteristic $p>0$ has universally trivial Chow group of $0$-cycles, the cohomological Brauer group of $X$ is universally trivial as…

Let $k$ be the function field of a complex curve or the field $C((t))$. We show that for a smooth complete intersection $X$ of $r$ hypersurfaces in $P^n_k$ of respective degrees $d_1,...,d_r$ with $\sum d_i^2\leq n+1$ the R-equivalence on…

We determine the Chow group of zero-cycles on a rational surface X defined over a finite extension K of the field of p-adic numbers (p a prime) when X is split by an unramified extension of K.

Let $X$ be a $K3$ surface over a $p$-adic field $k$ such that for some abelian surface $A$ isogenous to a product of two elliptic curves, there is an isomorphism over the algebraic closure of $k$ between $X$ and the Kummer surface…

In this note we are going to consider a smooth projective surface equipped with an involution and study the action of the involution at the level of Chow group of zero cycles.