Related papers: The Chow group of zero-cycles on certain Ch{\^a}te…

In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0$, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when…

The Chow rings of hyperK\"ahler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First we prove…

We use the elements in $K$-cohomology groups which are constructed by Flach and Mildenhall to obtain a finiteness result for the torsion part of the Chow group of a self-product of a modular curve.

Given an action of the one-dimensional torus on a projective variety, the associated Chow quotient arises as a natural parameter space of invariant $1$-cycles, which dominates the GIT quotients of the variety. In this paper we explore the…

We compute the cyclic and Hochschild cohomology groups for the algebras $\mathcal A_\theta^{alg} \rtimes \mathbb Z_3, \mathcal A_\theta^{alg} \rtimes \mathbb Z_4$ and $\mathcal A_\theta^{alg} \rtimes \mathbb Z_6$. We also compute the…

We define a family of arithmetic zero cycles in the arithmetic Chow group of a modular curve X_0(N), for N>3 odd and squarefree, and identify the arithmetic degrees of these cycles as q-coefficients of the central derivative of a Siegel…

We show that the chow group of $p$-cycles with rational coefficients are isomorphic to the corresponding rational homology groups for smooth complex projective varieties carrying a holomorphic vector field with an isolated zero locus. As…

Let $X$ be a smooth projective surface over a number field $K$. Assume that $X$ has an elliptic fibration over $\mathbb{P}^1_K$ with at least one singular fibre and a section. Let $\mathcal{X}/U$ be a smooth projective model of $X$ over…

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…

Using Bloch-Ogus theorem and Chern character from K-theory to cyclic homology, we answer a question of Green and Griffiths on extending Bloch formula. Moreover, we construct a map from local Hilbert functor to local cohomology. With…

The article considers the procedure of connection of graphs to the edges of a cyclic graph and its influence on the sandpile group of the graph thus obtained. A series of classes of graphs CH_n(a_1,...,a_n) is defined. Recurrent and…

Leech's (co)homology groups of finite cyclic monoids are computed.

Motivated by the generalized Bloch conjecture, we formulate a conjecture about the Chow groups of Pl\"ucker hypersurfaces in Grassmannians. We prove weak versions of this conjecture.

In this paper we extend Gazaki's results on the Chow groups of abelian varieties to the higher Chow groups. We introduce a Gazaki type filtration on the higher Chow group of zero-cycles on an abelian variety, whose graded quotients are…

We compute the Chow groups of smooth Gushel-Mukai varieties of dimension $5$.

We compute the integral Chow ring of the stack of smooth, non-hyperelliptic curves of genus three. We obtain this result by computing the integral Chow ring of the stack of smooth plane quartics, by means of equivariant intersection theory.

We study the restriction map to the closed fiber of a regular projective scheme over an excellent henselian discrete valuation ring, for a cohomological version of the Chow group of relative zero-cycles. Our main result extends the work of…

A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a…

In this exposition we understand when the natural map from the Chow variety parametrizing codimension $p$ cycles on a smooth projective variety $X$ to the Chow group $\CH^p(X)$ is surjective. We derive some consequences when the map is…

We prove that a smooth proper universally CH_0-trivial variety X over a field k has universally trivial Brauer group. This fills a gap in the literature concerning the p-torsion of the Brauer group when k has characteristic p.