The tautological ring of
We describe the tautological ring of the moduli space of stable -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.
Theta functions and cycles on some abelian fourfolds.
Torsion algebraic cycles and a theorem of Roitman
Torsion in CH2 of Severi-Brauer varieties and indecomposability of generic algebras.
Torsion in K2 of fields and 0-cycles on rational surfaces.
Trace Formula for Vanishing Cycles of Curves.
Transcendence degree of zero-cycles and the structure of Chow motives
In the paper we introduce a transcendence degree of a zero-cycle on a smooth projective variety X and relate it to the structure of the motive of X. In particular, we show that in order to prove Bloch’s conjecture for a smooth projective complex surface X of general type with p g = 0 it suffices to prove that one single point of a transcendence degree 2 in X(ℂ), over the minimal subfield of definition k ⊂ ℂ of X, is rationally equivalent to another single point of a transcendence degree zero over...
Twisted gamma filtration and algebras with orthogonal involution
For the Grothendieck group of a split simple linear algebraic group, the twisted γ-filtration provides a useful tool for constructing torsion elements in -rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the γ-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construction in the HSpin case previously obtained by Zainoulline.
Vanishing cycles for formal schemes.
Variations de structure de Hodge et zéro-cycles sur les surfaces générales.
Variations on a theme of rationality of cycles
We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s...
Variations on a Theorem of Abel.
Zero cycles and complete intersections on singular varieties.
Zero cycles and the number of generators of an ideal
Zero cycles on a singular surface. I. Appendix: Chow groups of rational surfaces with rational double points.
Zero cycles on a singular surface. II.
Zero cycles on algebraic varieties in nonzero characteristic : Rojtman's theorem
Zero cycles on certain singular elliptic surfaces
Zero cycles on surfaces with
Zero-cycles and rational points on some surfaces over a global function field