Ein ?Descente"-Lemma und Grothendiecks Projektionssatz für nicht-noethersche Schemata.
Einfach-elliptische Singularitäten.
Embedding-obstruction for products of non-singular, projective varieties.
Excellent connections in the motives of quadrics
In this article we prove the conjecture claiming that the motive of a real quadric is the “most decomposable” among anisotropic quadrics of given dimension over all fields. This imposes severe restrictions on the motive of arbitrary anisotropic quadric. As a corollary we estimate from below the rank of indecomposable direct summand in the motive of a quadric in terms of its dimension. This generalizes the well-known Binary Motive Theorem. Moreover, we have the description of the Tate motives involved....
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 finitely generated over ℚ and X → C is a quadric fibration of odd relative dimension at least 11, then CH i(X) is finitely generated for i ≤ 4.
Fondements de la géométrie algébrique. Commentaires
Formes quadratiques et cycles algébriques
Introduite par Witt en 1937, la théorie des formes quadratiques sur un corps joue un rôle central dans la démonstration des conjectures de Milnor par Voevodsky via les travaux pionniers de Rost qui y interviennent. Réciproquement, les méthodes de Rost et Voevodsky utilisant la théorie des motifs et les opérations de Steenrod motiviques révolutionnent la théorie des formes quadratiques et ont conduit à la démonstration de résultats de base qui semblaient auparavant inaccessibles. On expliquera notamment...
Formes quadratiques multiplicatives et variétés algébriques : deux compléments
Gersten's conjecture and the homology of schemes
Hilbert's Theorem 90 for K2, with Application to the Chow Groups of Rational Surfaces.
Holes in
Homological equivalence modulo algebraic equivalence is not finitely generated
Intersection rings of spaces of triangles
-invariant of linear algebraic groups
Let be a semisimple linear algebraic group of inner type over a field , and let be a projective homogeneous -variety such that splits over the function field of . We introduce the -invariant of which characterizes the motivic behavior of , and generalizes the -invariant defined by A. Vishik in the context of quadratic forms. We use this -invariant to provide motivic decompositions of all generically split projective homogeneous -varieties, e.g. Severi-Brauer varieties, Pfister quadrics,...
K2-Cohomology and the Second Chow Group.
K3 surfaces: moduli spaces and Hilbert schemes.
Kolyvagin's method for Chow groups of Kuga-Sato varieties.
La classe fondamentale d'un cycle
La -équivalence sur les tores
Le théorème de Riemann-Roch pour les variétés algébriques éventuellement singulières