Tautological Cycles on Jacobian Varieties
The arithmetic of zero cycles on surfaces with geometric genus and irregularity zero.
The coniveau filtration and non-divisibility for algebraic cycles.
The Euler series of restricted Chow varieties
The generalized Hodge and Bloch conjectures are equivalent for general complete intersections
We prove that Bloch’s conjecture is true for surfaces with obtained as -sets of a section of a very ample vector bundle on a variety with “trivial” Chow groups. We get a similar result in presence of a finite group action, showing that if a projector of the group acts as on holomorphic -forms of , then it acts as on -cycles of degree of . In higher dimension, we also prove a similar but conditional result showing that the generalized Hodge conjecture for general implies the...
The Lê varieties, I.
The local monodromy as a generalized algebraic correspondence (with an appendix by Spencer Bloch).
The modified diagonal cycle on the triple product of a pointed curve
Let be a curve over a field with a rational point . We define a canonical cycle . Suppose that is a number field and that has semi-stable reduction over the integers of with fiber components non-singular. We construct a regular model of and show that the height pairing is well defined where and are correspondences. The paper ends with a brief discussion of heights and -functions in the case that is a modular curve.
The rank-one limit of the Fourier-Mukai transform.
The spectral sequence relating algebraic K-theory to motivic cohomology
The structure of a local embedding and Chern classes of weighted blow-ups
For a proper local embedding between two Deligne-Mumford stacks and , we find, under certain mild conditions, a new (possibly non-separated) Deligne-Mumford stack , with an etale, surjective and universally closed map to the target , and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to . Moreover, a natural set of weights on the substacks of allows the construction of a universally closed...
The Tate conjecture for ordinary K3 surfaces over finite fields.
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.