46 citations · 74 across the 18 of their papers we have counts for
19 papers
Arithmetic of Gysin kernels
Vladimir Guletskii, Bo Zhang
Let be a field, and let be a smooth projective surface over . Fix a Lefschetz pencil on , and let be its fibre at the generic point of . The closed i…
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.
The tangent space to the space of 0-cycles
Vladimir Guletskii
Let be a Noetherian scheme, and let be a scheme over . Under mild assumptions, one can construct the connected infinite symmetric power , whose…
Bloch's conjecture for surfaces with involutions and of geometric genus zero
Vladimir Guletskii
Let be a smooth projective surface with , let be a regular involution acting on , and let be the resolution of singularities of the quotient surface . In…
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.
Motivic obstruction to rationality of a general cubic hypersurface in
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…
-connectivity on Chow monoids v.s. rational equivalence of algebraic cycles
Vladimir Guletskii
Let be a field of characteristic zero, and let be a projective variety embedded into a projective space over . For two natural numbers and let be th…
Étale monodromy and rational equivalence for -cycles on cubic hypersurfaces in
Kalyan Banerjee, Vladimir Guletskii
Let be an uncountable algebraically closed field of characteristic , and let be a smooth projective connected variety of dimension , appropriately embedded into $\ma…
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…
Positive model structures for abstract symmetric spectra
Sergey Gorchinskiy, Vladimir Guletskii
We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based o…
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…
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…
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…
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…
On the continuous part of codimension two algebraic cycles on threefolds over a field
Vladimir Guletskii
Let be a non-singular projective threefold over an algebraically closed field of any characteristic, and let be the group of algebraically trivial codimension 2 algebr…
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…
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…
Finite dimensional objects in distinguished triangles
Vladimir Guletskii
We prove an additivity for evenly (oddly) finite dimensional objects in distinguished triangles in a triangulated monoidal category structured by an underlying model monoidal categ…
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…