Milnor’s conjecture on quadratic forms and motivic complexes
Motifs de dimension finie
On sait que les groupes de Chow d’une variété projective ne sont pas de type fini, et ne peuvent même être paramétrés par une variété algébrique, en général. Pourtant, S.-I. Kimura et P. O’Sullivan ont conjecturé (indépendamment l’un de l’autre) que les motifs de Chow, définis en termes de correspondances algébriques modulo l’équivalence rationnelle, sont de “dimension finie”au sens où, tout comme les super-fibrés vectoriels, ils sont somme d’un facteur dont une puissance extérieure est nulle et...
Motifs Génériques
Motivic cell structures.
Motivic cohomology and unramified cohomology of quadrics
This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension and . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real quadrics....
Motivic cohomology with -coefficients
Motivic functors.
Motivic Landweber exactness.
Motivic measures
Motivic symmetric spectra.
Motivic tubular neighborhoods.
Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields.
Nilpotence, radicaux et structures monoïdales
On non-commutative twisting in étale and motivic cohomology
This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups , where is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.
On the Euler-Poincaré characteristics of finite dimensional -adic Galois representations
On the motivic spectra representing algebraic cobordism and algebraic -theory.
On the Shafarevich and Tate conjectures for hyperkähler varieties.
Periodicity in -groups of certain fields
Reduced power operations in motivic cohomology
Slices and transfers.