Related papers: Zero cycles with modulus and zero cycles on singul…

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…

We show that the Chow group of 0-cycles on a singular projective scheme $X$ over a finite field describes the abelian extensions of its function field which are unramified over the regular locus of $X$. As a consequence, we obtain the…

We prove that all points of a toroidal compactification lying over 0-dimensional cusps are rationally equivalent in the integral Chow group for most classical modular varieties (Siegel, Hilbert, orthogonal, Hermitian, quaternionic). This…

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…

We prove Bloch's formula for the Chow group of 0-cycles with modulus on a smooth quasi-projective surface over a field. We use this formula to give a simple proof of the rank one case of a conjecture of Deligne and Drinfeld on lisse…

We introduce a new obstruction to the existence of a universal $0$-cycle on a smooth projective complex variety. As an application, we construct a smooth projective complex surface whose Chow group of $0$-cycles is representable but which…

Let $X$ be a product of smooth projective curves over a finite unramified extension $k$ of $\mathbb{Q}_p$. Suppose that the Albanese variety of $X$ has good reduction and that $X$ has a $k$-rational point. We propose the following…

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of…

We study the Chow group of zero-cycles on singular varieties using the cdh topology. We define the cdh versions of the zero-cycles and albanese maps. We prove results comparing these groups for a singular variety with the similar groups on…

For a generalized Kummer variety X of dimension 2n, we will construct for each 0 < i < n some co-isotropic subvarieties in X foliated by i-dimensional constant cycle subvarieties. These subvarieties serve to prove that the rational orbit…

For a smooth projective variety $X$ over a number field $k$ a conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map of $X$ is a torsion group. In this article we consider a product $X=C_1\times\cdots\times C_d$ of…

We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on…

We prove the existence of a canonical zero-cycle on a Calabi-Yau hypersurface X in a complex projective homogeneous variety. More precisely, we show that the intersection of any n divisors on X, n=dim X, is proportional to the class of a…

The notion of modulus is a striking feature of Rosenlicht-Serre's theory of generalized Jacobian varieties of curves. It was carried over to algebraic cycles on general varieties by Bloch-Esnault, Park, R\"ulling, Krishna-Levine. Recently,…

We study the deformations of the Chow group of zero-cycles of the special fibre of a smooth scheme over a henselian discrete valuation ring. Our main tools are Bloch's formula and differential forms. As a corollary we get an algebraization…

We show that every cycle in the degree $d$ algebraic cobordism group $\Omega_d(X)$ of a smooth projective variety $X$ over a field of characteristic $0$ is smoothable when $2d<\dim(X)$, that is, it can be written as a linear combination of…

Let $k$ be a field and let $\Omega$ be a universal domain over $k$. Let $f:X \r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $\leq 2$ such that the general…

Let \(A\) be a central simple algebra over a field \(F\) with index \(n\) and let \(\mathrm{SB}_r(A)\) denote the \(r\)-th generalized Severi--Brauer variety associated with \(A\). We prove that the Chow group of zero cycles of degree zero…

Associated to an algebraic curve $X$, there are two canonically constructed homologically trivial algebraic $1$-cycles, the Ceresa cycle in the Jacobian of $X$, and the Gross-Kudla-Schoen modified diagonal cycle in the triple product $X…

We study the Chow group of zero-cycles of smooth projective varieties over local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with…