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A commutative regulator map into Deligne–Beilinson cohomology
Bloch (The Lefschetz centennial conference, part I (Mexico City, 1984), volume 58 of contemporary mathematics. American Mathematical Society,...
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UNITARY GRASSMANNIANS OF DIVISION ALGEBRAS
We consider a central division algebra over a separable quadratic extension of a base field endowed with a unitary involution and prove...
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Yet another version of Mumford’s theorem
The aim of this note is to provide a variant statement of Mumford’s theorem. This variant states that for a general variety, all Chow groups are “as...
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Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves
We analyze Weierstrass cycles and tautological rings in moduli spaces of smooth algebraic curves and in moduli spaces of integral algebraic curves...
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Incompressibility of products of Weil transfers of generalized Severi–Brauer varieties
We generalize the result of Karpenko and Reichstein (
2014 ) on incompressibility of Galois Weil transfer of generalized Severi–Brauer varieties to... -
On the interior motive of certain Shimura varieties: the case of Picard surfaces
The purpose of this article is to construct a Hecke-equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Picard...
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Décomposition de motifs abéliens
Let A be an abelian variety and let us fix a Weil cohomology with coefficients in F . Let H 1 ( A , F ) be the first cohomology group of A and
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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...
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Lagrangian 4-planes in holomorphic symplectic varieties of K3[4]-type
We classify the cohomology classes of Lagrangian 4-planes ℙ 4 in a smooth manifold X deformation equivalent to a Hilbert scheme of four points on a K3...
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Cycle modules and the intersection A ∞-algebra
In his paper Chow Group with Coefficients , M. Rost has developed a generalization of the classical Chow groups based on Milnor K-theory and an...
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Around rationality of cycles
We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have...
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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...
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The J-invariant and Tits algebras for groups of inner type E 6
A connection between the indices of the Tits algebras of a split linear algebraic group G and the degree one parameters of its motivic J -invariant...
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Hyperbolicity of unitary involutions
We prove the so-called Unitary Hyperbolicity Theorem , a result on hyperbolicity of unitary involutions. The analogous previously known results for...
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Seshadri positive submanifolds of polarized manifolds
Let Y be a submanifold of dimension y of a polarized complex manifold ( X, A ) of dimension k ≥ 2, with 1 ≤ y ≤ k −1. We define and study two positivity...
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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 ....
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On the finite dimensionality of a K3 surface
For a smooth projective surface X the finite dimensionality of the Chow motive h ( X ), as conjectured by Kimura, has several geometric consequences....
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Algebraic cycles on the generic abelian fourfold with polarization of type (1,2,2,2)
In this paper we construct a non-torsion element in the higher Griffiths group Griff 3,2 ( A 4 ) for the generic abelian fourfold A ...
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On the André motive of certain irreducible symplectic varieties
We show that if Y is an algebraic deformation of the Hilbert scheme of points on a K3 surface, then the André motive of Y is an object of the...