V. Guletskiĭ

activity

20032026

most citedFinite dimensional motives and the Conjectures of Beilinson and Murre

46 citations · 74 across the 18 of their papers we have counts for

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17 papers · 1 filter

math.AG2026

Arithmetic of Gysin kernels

Vladimir Guletskii, Bo Zhang

Let $k$ be a field, and let $X$ be a smooth projective surface over $k$ . Fix a Lefschetz pencil on $X$ , and let $C$ be its fibre at the generic point of $P^{1}$ . The closed i…

math.AG2025

The Bloch conjecture

Vladimir Guletskii

We prove the conjecture stated by Spencer Bloch in 1975 and saying that the Albanese kernel of a smooth projective surface is 0, provided its second cohomology group is algebraic.

math.AG2018

The tangent space to the space of 0-cycles

Vladimir Guletskii

Let $S$ be a Noetherian scheme, and let $X$ be a scheme over $S$ . Under mild assumptions, one can construct the connected infinite symmetric power $Sym^{\infty} (X / S)$ , whose…

math.AG2017★ 4 cited

Bloch's conjecture for surfaces with involutions and of geometric genus zero

Vladimir Guletskii

Let $S$ be a smooth projective surface with $p_{g} = 0$ , let $ι$ be a regular involution acting on $S$ , and let $W$ be the resolution of singularities of the quotient surface $S / ι$ . In…

math.AG2016★ 7 cited

Bloch's conjecture for the surface of Craighero and Gattazzo

Vladimir Guletskii

The goal of this paper is to prove Bloch's conjecture for the numerical Godeaux surface constructed by P. Craighero and R. Gattazzo.

math.AG2016

Motivic obstruction to rationality of a general cubic hypersurface in $P^{5}$

Vladimir Guletskii

We introduce integrally essentially indecomposable motives and prove that, if the integral motive of a smooth projective surface over a field of sufficiently big transcendence degr…

math.AG2014

$A^{1}$ -connectivity on Chow monoids v.s. rational equivalence of algebraic cycles

Vladimir Guletskii

Let $k$ be a field of characteristic zero, and let $X$ be a projective variety embedded into a projective space over $k$ . For two natural numbers $r$ and $d$ let $C_{r, d} (X)$ be th…

math.AG2014★ 1 cited

Étale monodromy and rational equivalence for $1$ -cycles on cubic hypersurfaces in $P^{5}$

Kalyan Banerjee, Vladimir Guletskii

Let $k$ be an uncountable algebraically closed field of characteristic $0$ , and let $X$ be a smooth projective connected variety of dimension $2 p$ , appropriately embedded into $\ma…

math.AG2011★ 5 cited

Algebraic cycles on quadric sections of cubics in P^4 under the action of symplectomorphisms

V. Guletskii, A. Tikhomirov

We consider the involution changing the sign of two coordinates in 4-dimensional projective space. The intersection S of invariant cubic and quadric hypersurfaces in P^4 is a K3-su…

math.AG2010

Transcendence degree of zero-cycles and the structure of Chow motives

Sergey Gorchinskiy, Vladimir Guletskii

We show how the notion of the transcendence degree of a zero-cycle on a smooth projective variety X is related to the structure of the motive M(X). This can be of particular intere…

math.AG2010★ 1 cited

Non-trivial elements in the Abel-Jacobi kernels of higher dimensional varieties

Sergey Gorchinskiy, Vladimir Guletskii

The purpose of this paper is to construct non-trivial elements in the Abel-Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical inva…

math.AG2009

Symmetric powers in abstract homotopy categories

Sergey Gorchinskiy, Vladimir Guletskii

We study symmetric powers in the homotopy categories of abstract closed symmetric monoidal model categories, in both unstable and stable settings. As an outcome, we prove that symm…

math.AG2008★ 4 cited

Motives and representability of algebraic cycles on threefolds over a field

S. Gorchinskiy, V. Guletskii

We study links between algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in Q. We decompose the motive of a non-singular projective threef…

math.AG2006★ 1 cited

On the continuous part of codimension two algebraic cycles on threefolds over a field

Vladimir Guletskii

Let $X$ be a non-singular projective threefold over an algebraically closed field of any characteristic, and let $A^{2} (X)$ be the group of algebraically trivial codimension 2 algebr…

math.AG2006

Zeta functions in triangulated categories

Vladimir Guletskii

We prove 2-out-of-3 property for rationality of motivic zeta function in distinguished triangles in Voevodsky's category DM. As an application, we show rationality of motivic zeta…

math.AG2005

Motives of smooth families and cycles on threefolds

Vladimir Guletskii

Let X --> S be a smooth projective family of surfaces over a smooth curve S such that the generic fiber is a surface with Weil H^2 spanned by divisors and trivial H^1. We prove tha…

math.AG2003★ 46 cited

Finite dimensional motives and the Conjectures of Beilinson and Murre

Vladimir Guletskii, Claudio Pedrini

We relate the notion of finite dimensionality of the Chow motive M(X) of a smooth projective variety X (as defined by S. Kimura) with the Conjectures of Beilinson, Bloch and Murre…

Arithmetic of Gysin kernels

The Bloch conjecture

The tangent space to the space of 0-cycles

Bloch's conjecture for surfaces with involutions and of geometric genus zero

Bloch's conjecture for the surface of Craighero and Gattazzo

Motivic obstruction to rationality of a general cubic hypersurface in P5

A1-connectivity on Chow monoids v.s. rational equivalence of algebraic cycles

Étale monodromy and rational equivalence for 1-cycles on cubic hypersurfaces in P5

Algebraic cycles on quadric sections of cubics in P^4 under the action of symplectomorphisms

Transcendence degree of zero-cycles and the structure of Chow motives

Non-trivial elements in the Abel-Jacobi kernels of higher dimensional varieties

Symmetric powers in abstract homotopy categories

Motives and representability of algebraic cycles on threefolds over a field

On the continuous part of codimension two algebraic cycles on threefolds over a field

Zeta functions in triangulated categories

Motives of smooth families and cycles on threefolds

Finite dimensional motives and the Conjectures of Beilinson and Murre

Motivic obstruction to rationality of a general cubic hypersurface in $P^{5}$

$A^{1}$ -connectivity on Chow monoids v.s. rational equivalence of algebraic cycles

Étale monodromy and rational equivalence for $1$ -cycles on cubic hypersurfaces in $P^{5}$