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Rationality of Fano Threefolds of Degree 18 over Non-closed Fields
We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.
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Vanishing Cycles under Base Change and the Integral Hodge Conjecture
In this paper we discuss an obstruction to the integral Hodge conjecture which arises from a certain behavior of vanishing cycles. This allows us to...
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Compatibility of weak approximation for zero-cycles on products of varieties
The Brauer-Manin obstruction is conjectured to be the only obstruction to weak approximation for zero-cycles on proper smooth varieties defined over...
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A Survey of the Additive Dilogarithm
Borel’s construction of the regulator gives an injective map from the algebraic K–groups of a number field to its Deligne–Beilinson cohomology...
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Linear forms, algebraic cycles, and derivatives of L-series
In this note, we state some refinements of conjectures of Gan-Gross-Prasad and Kudla concerning the central derivatives of L-series and special...
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Cohomologie non ramifiée dans le produit avec une courbe elliptique
A method of Gabber (Enseign Math (2) 48(1–2):127–146,
2002 ) produces unramified cohomology classes in the products of certain varieties with an... -
Unramified Cohomology, Algebraic Cycles and Rationality
This is a survey on unramified cohomology with a view towards its applications to rationality problems.
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Supersingular Irreducible Symplectic Varieties
In complex geometry, irreducible holomorphic symplectic varieties, also known as compact hyper-Kähler varieties, are natural higher-dimensional...
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On the Image of the Second l-adic Bloch Map
For a smooth projective geometrically uniruled threefold defined over a perfect field we show that there exists a canonical abelian variety over the...
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Tautological ring of strata of differentials
Strata of k -differentials on smooth curves parameterize sections of the k -th power of the canonical bundle with prescribed orders of zeros and poles....
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Motives of moduli spaces on K3 surfaces and of special cubic fourfolds
For any smooth projective moduli space M of Gieseker stable sheaves on a complex projective K3 surface (or an abelian surface) S , we prove that the...
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On generic flag varieties of Spin(11) and Spin(12)
Let X be the variety of Borel subgroups of a split semisimple algebraic group G over a field, twisted by a generic G -torsor. Conjecturally, the...
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A remark on Beauville’s splitting property
Let X be a hyperkähler variety. Beauville has conjectured that a certain subring of the Chow ring of X should inject into cohomology. This note...
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Symmetric correspondences on quadrics
We prove a result comparing the rationality of some elementary algebraic cycles introduced by Alexander Vishik, defined on orthogonal grassmannians,...
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Algebraic Cycles on Fano Varieties of Some Cubics
We study cycle-theoretic properties of the Fano variety of lines on a smooth cubic fivefold. The arguments are based on the fact that this Fano...
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On the Chow groups of certain cubic fourfolds
This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic...
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Relative singular support and the semi-continuity of characteristic cycles for étale sheaves
Recently, the singular support and the characteristic cycle of an étale sheaf on a smooth variety over a perfect field are constructed by Beilinson...
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Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane
We prove the universal triviality of the third unramified cohomology group of a very general complex cubic fourfold containing a plane. The proof...
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A family of K3 surfaces having finite-dimensional motive
This short note contains an example of a 4-dimensional family of K 3 surfaces having finite-dimensional motive. Some consequences are presented, for...