[Motifs et modules sur la cohomologie motivique]
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 , pour k un corps de caractéristique zéro, la catégorie homotopique obtenue est équivalente à la grande catégorie des motifs introduite par Voevodsky.
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 , for k a field of characteristic zero, the corresponding homotopy category is equivalent to Voevodsky's big category of motives.
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@article{CRMATH_2006__342_10_751_0,
author = {R\"ondigs, Oliver and {\O}stv{\ae}r, Paul Arne},
title = {Motives and modules over motivic cohomology},
journal = {Comptes Rendus. Math\'ematique},
pages = {751--754},
publisher = {Elsevier},
volume = {342},
number = {10},
year = {2006},
doi = {10.1016/j.crma.2006.03.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.03.013/}
}
TY - JOUR AU - Röndigs, Oliver AU - Østvær, Paul Arne TI - Motives and modules over motivic cohomology JO - Comptes Rendus. Mathématique PY - 2006 SP - 751 EP - 754 VL - 342 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.03.013/ DO - 10.1016/j.crma.2006.03.013 LA - en ID - CRMATH_2006__342_10_751_0 ER -
%0 Journal Article %A Röndigs, Oliver %A Østvær, Paul Arne %T Motives and modules over motivic cohomology %J Comptes Rendus. Mathématique %D 2006 %P 751-754 %V 342 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.03.013/ %R 10.1016/j.crma.2006.03.013 %G en %F CRMATH_2006__342_10_751_0
Röndigs, Oliver; Østvær, Paul Arne. Motives and modules over motivic cohomology. Comptes Rendus. Mathématique, Tome 342 (2006) no. 10, pp. 751-754. doi : 10.1016/j.crma.2006.03.013. http://www.numdam.org/articles/10.1016/j.crma.2006.03.013/
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