The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over ) of the corresponding cobordism groups over Spec() for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.
Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.
Let be a field. We compute the set ofnaivehomotopy classes of pointed -scheme endomorphisms of the projective line . Our result compares well with Morel’s computation in [11] of thegroup of -homotopy classes of pointed endomorphisms of : the set admits an a priori monoid structure such that the canonical map is a group completion.
We relate -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
We construct for a real algebraic variety (or more generally for a scheme essentially of finite type over a field of characteristic ) complexes of algebraically and - algebraically constructible chains. We study their functoriality and compute their homologies for affine and projective spaces. Then we show that the lagrangian algebraically constructible cycles of the cotangent bundle are exactly the characteristic cycles of the algebraically constructible functions.
À toute classe dans le groupe de Brauer d’un corps sont associés deux entiers, l’indice (degré d’un corps gauche représentant la classe) et l’exposant (ordre de la classe dans le groupe de Brauer). L’exposant divise l’indice, mais ne lui est pas nécessairement égal. Lorsque est un corps de nombres, c’est un théorème des années 1930 qu’exposant et indice coïncident. A. J. de Jong (Duke Math. J. 123 (2004) 71-94) a montré récemment qu’ils coïncident aussi lorsque est un corps de fonctions de...