Motivic Landweber exactness.
Motivic symmetric spectra.
Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields.
On extensions of mixed motives.
In this article we give an introduction to mixed motives and sketch a couple of ways to construct examples.
On the Chow groups of quadratic Grassmannians.
On the cyclic homology of ringed spaces and schemes.
On the group .
Periodicity in -groups of certain fields
Pour une théorie inconditionnelle des motifs
Proof of Nadel’s conjecture and direct image for relative -theory
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
Propriétés du groupe tannakien des structures de Hodge -adiques et torseur entre cohomologies cristalline et étale
On donne des propriétés de la catégorie tannakienne des modules de Dieudonné filtrés sur un corps -adique (ces modules de Dieudonné jouent en -adique un rôle analogue aux structures de Hodge complexes). On prouve l’existence d’un foncteur fibre sur et la simple connexité du groupe associé. Ceci permet de montrer, sous la conjecture de Fontaine : “faiblement admissible entraîne admissible”, une conjecture de Rapoport et Zink décrivant le torseur entre cohomologie cristalline et étale, et de prouver...
Reduced power operations in motivic cohomology
Riemann-Roch type theorems for arithmetic schemes with a finite group action.
Rigidity II: non-orientable case.
Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve.
Slices and transfers.
Strong separativity over exchange rings
An exchange ring is strongly separative provided that for all finitely generated projective right -modules and , . We prove that an exchange ring is strongly separative if and only if for any corner of , implies that there exist such that and if and only if for any corner of , implies that there exists a right invertible matrix . The dual assertions are also proved.
Sur les extensions totalement décomposées de certains corps de fonctions
The Chern character for Lie-Rinehart algebras
Let be a commutative -algebra where is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a -connection. Our result generalizes the classical Chern character from the -theory of to the algebraic De Rham cohomology.
The connection between the -theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel