Algebraic cycles on a general complete intersection of high multi-degree of a smooth projective variety
Algebraic cycles on certain Calabi-Yau threefolds.
Algebraic, Rational, and homological equivalence of real cycles.
Algebraicity Criteria for Compact Complex Manifolds.
An effective version of Nor's theorem.
Arithmetic intersection theory
Arithmetic of 0-cycles on varieties defined over number fields
Let be a rationally connected algebraic variety, defined over a number field We find a relation between the arithmetic of rational points on and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for -rational points on for all finite extensions (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree...
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 already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.
Bemerkungen über den Zusammenhang der Flächen
Birational geometry of quadrics
We construct new birational maps between quadrics over a field. The maps apply to several types of quadratic forms, including Pfister neighbors, neighbors of multiples of a Pfister form, and half-neighbors. One application is to determine which quadrics over a field are ruled (that is, birational to the projective line times some variety) in a larger range of dimensions. We describe ruledness completely for quadratic forms of odd dimension at most 17, even dimension at most 10, or dimension 14....
Chow-Künneth decomposition for some moduli spaces.
Classes caractéristiques secondaires des fibrés plats
Correspondence homomorphisms for singular varieties
We study certain kinds of geometric correspondences between (possibly singular) algebraic varieties and we obtain comparison results regarding natural filtrations on the homology of varieties.
Cycle exceptionnel de l’éclatement d’un idéal définissant l’origine de et applications
Soit un idéal de définissant l’origine de . On donne une méthode explicite pour déterminer, après un choix convenable des générateurs de , le cycle de sous-jacent à la fibre exceptionnelle de l’éclatement de relativement à . On étudie également l’éclatement d’une famille équimultiple d’idéaux ponctuels paramétrée par un germe d’espace analytique complexe réduit.
Cycles, L-functions and triple products of elliptic curves.
Cycles of algebraic manifolds and -cohomology
Deformation to the normal cone, rationality and the Stückrad-Vogel cycle.
Differential Equations associated to Families of Algebraic Cycles
We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.
Dimensions of anisotropic indefinite quadratic forms. II.
Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini