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

Gorchinskiy Sergey; Guletskii V.

?

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

Central European Journal of Mathematics. 2012. Vol. 10. No. 2. P. 559–568.

Gorchinskiy Sergey, Guletskii V.

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 interest in the context of Bloch's conjecture, especially for Godeaux surfaces, when the surface is given as a finite quotient of a suitable quintic in P^3.

Language: English

Keywords: algebraic cycle

Integral Chow motives of threefolds with K-motives of unit type

Gorchinskiy S., Bulletin of the Korean Mathematical Society 2017 Vol. 54 No. 5 P. 1827–1849

We prove that if a smooth projective algebraic variety of dimension less or equal to three has a unit type integral K-motive, then its integral Chow motive is of Lefschetz type. As a consequence, the integral Chow motive is of Lefschetz type for a smooth projective variety of dimension less or equal to three that ...

Added: October 17, 2017

Algebraic Cycles on Quadric Sections of Cubics in ℙ4 under the Action of Symplectomorphisms

Guletski ̆i V., Tikhomirov A. S., Proceedings of the Edinburgh Mathematical Society 2016 Vol. 59 No. 02 P. 377–392

Let τ be the involution changing the sign of two coordinates in ℙ4. We prove that τ induces the identity action on the second Chow group of the intersection of a τ-invariant cubic with a τ-invariant quadric hypersurface in ℙ4. Let lτ andΠτ be the one- and two-dimensional components of the fixed locus of the involution τ. We describe the generalized Prymian associated with the ...

Added: December 28, 2015

Hodge realizations of 1-motives and the derived Albanese

Vologodsky V., K-Theory 2012 Vol. 10 No. 2 P. 371–412

We prove that the embedding of the derived category of 1-motives up to isogeny into the triangulated category of effective Voevodsky motives, as well as its left adjoint functor LAlb ℚ, commute with the Hodge realization. This result yields a new proof of the rational form of Deligne's conjecture on 1-motives. ...

Added: December 17, 2015

Product structures in motivic cohomology and higher Chow groups

Kondo S., Yasuda S., Journal of Pure and Applied Algebra 2011 Vol. 215 No. 4

It is shown that the product structures of motivic cohomology groups and of higher Chow groups are compatible under the comparison isomorphism of Voevodsky (2002) [11]. This extends the result of Weibel (1999) [14], where he used the comparison isomorphism which assumed that the base field admits resolution of singularities. The mod nn motivic cohomology groups ...

Added: September 22, 2014

The Riemann–Roch theorem without denominators in motivic homotopy theory

Kondo S., Yasuda S., Journal of Pure and Applied Algebra 2014 No. 218 P. 1478–1495

The Riemann–Roch theorem without denominators for the Chern class maps on higher algebraic K-groups with values in motivic cohomology groups in the context of motivic homotopy theory is proved. ...

Added: September 22, 2014

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

Gorchinskiy Sergey, Guletskii V., Advances in Mathematics 2013 Vol. 241 P. 162–191

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 invariants at points with different transcendence degrees over a subfield in C. ...

Added: October 14, 2013

Motives and representability of algebraic cycles on threefolds over a field

Gorchinskiy Sergey, Guletskii V., Journal of Algebraic Geometry 2012 Vol. 21 No. 2 P. 347–373

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 threefold X with representable algebraic part of CH_0(X) into Lefschetz motives and the Picard motive of a certain abelian variety, isogenous to the corresponding intermediate Jacobian J^2(X) when the ground ...

Added: February 5, 2013