Motives and modules over motivic cohomology

Oliver Röndigs; Paul Arne Østvær

doi:10.1016/j.crma.2006.03.013

Algebraic Geometry/Topology

Motives and modules over motivic cohomology
[Motifs et modules sur la cohomologie motivique]

Présenté par : Pierre Deligne

Oliver Röndigs ¹ ; Paul Arne Østvær ²

¹ Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
² Department of Mathematics, University of Oslo, NO-0316 Oslo, Norway

Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 751-754.

Abstract (VO)
Résumé

In this Note we summarize the main results and techniques in our homotopical algebraic approach to motives. A major part of this work relies on highly structured models for motivic stable homotopy theory. For any noetherian and separated base scheme of finite Krull dimension these frameworks give rise to a homotopy theoretic meaningful study of modules over motivic cohomology. When the base scheme is $Spec (k)$ , for k a field of characteristic zero, the corresponding homotopy category is equivalent to Voevodsky's big category of motives.

Dans cette Note, nous présentons nos résultats principaux et les techniques utilisées dans notre étude des motifs, qui est basée sur la théorie d'homotopie. Une partie importante de ce travail utilise des modèles hautement structurés pour la théorie d'homotopie stable motivique. Pour tout schéma de base noethérien, séparé et de dimension de Krull finie, ces outils permettent l'étude de la théorie d'homotopie des modules sur la cohomologie motivique. Lorsque le schéma de base est $Spec (k)$ , pour k un corps de caractéristique zéro, la catégorie homotopique obtenue est équivalente à la grande catégorie des motifs introduite par Voevodsky.

Reçu le : 2005-12-14
Accepté le : 2006-03-14
Publié le : 2006-04-18

DOI : 10.1016/j.crma.2006.03.013

Affiliations des auteurs :

Oliver Röndigs ¹ ; Paul Arne Østvær ²

¹ Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
² Department of Mathematics, University of Oslo, NO-0316 Oslo, Norway

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Oliver Röndigs; Paul Arne Østvær. Motives and modules over motivic cohomology. Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 751-754. doi : 10.1016/j.crma.2006.03.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.013/

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Bjørn Dundas; Michael Hill; Kyle Ormsby; Paul Østvær Hochschild homology of mod-𝑝 motivic cohomology over algebraically closed fields, Communications of the American Mathematical Society, Volume 4 (2024) no. 13, p. 578 | DOI:10.1090/cams/36
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Oliver Röndigs; Paul Arne Østvær Modules over motivic cohomology, Advances in Mathematics, Volume 219 (2008) no. 2, p. 689 | DOI:10.1016/j.aim.2008.05.013
Oliver Röndigs; Paul Arne Østvær Rigidity in motivic homotopy theory, Mathematische Annalen, Volume 341 (2008) no. 3, p. 651 | DOI:10.1007/s00208-008-0208-5

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