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Lifting of Coefficients for Chow Motives of Quadrics
We prove that the natural functor from the category of Chow motives of smooth projective quadrics with integral coefficients to the category with...
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Une version du théorème d’Amer et Brumer pour les zéro-cycles
M. Amer and A. Brumer have shown that, for two homogeneous quadratic forms f and g over a field k, the locus...
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Non-self-dual Stably Free Modules
We give several proofs that a stably free module of even rank need not be self-dual.
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Upper Motives of Outer Algebraic Groups
Let G be a semisimple affine algebraic group over a field F. Assuming that G becomes of inner type over some finite field extension of F of degree a...
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Remarks on Hard Lefschetz conjectures on Chow groups
We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are...
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Essential dimension of Hermitian spaces
Given an hermitian space we compute its essential dimension, Chow motive and prove its incompressibility in certain dimensions.
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Some remarks on the Hodge conjecture for abelian varieties
We show how the classical Hodge conjecture for the middle cohomology of an abelian variety is equivalent to the general Hodge conjecture for the...
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Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves
We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is...
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Some inequalities for Kodaira–Iitaka dimension on subvarieties
In this paper an investigation is presented of the relationship between the Kodaira–Iitaka dimension of a line bundle on an ambient normal variety...
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Self-Correspondences of K3 Surfaces via Moduli of Sheaves
Let X be an algebraic K3 surface with Picard lattice N(X), and M X (v) the moduli space of sheaves on X...
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Graph invariants and the positivity of the height of the Gross-Schoen cycle for some curves
Let X be a projective curve over a global field K . Gross and Schoen defined a modified diagonal cycle Δ on X 3 , and showed that the height
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Infinitesimal invariant and Massey products
In this work, we study the Griffiths infinitesimal invariant of the curve in the jacobian using secondary cohomology maps. In order to do this, we...
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Motives of some Fano varieties
We study the Fano varieties of projective k -planes lying in hypersurfaces and investigate the associated motives.
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Tautological cycles on Jacobian varieties
In this paper we study the algebraic structure of the Tautological ring of a Jacobian: by the use of hard-Lefschetz-primitive classes we construct...
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Chern invariants of some flat bundles in the arithmetic Deligne cohomology
In this note, we investigate the cycle class map between the rational Chow groups and the arithmetic Deligne cohomology, introduced by...
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Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. I
In this paper we construct and study the actions of certain deformations of the Lie algebra of Hamiltonians on the plane on the Chow groups (resp.,...