Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T23:15:05.301Z Has data issue: false hasContentIssue false
  • English
  • Français

Structure de poids à la Bondarko sur les motifs de Beilinson

Part of: (Co)homology theory General theory of categories and functors Abelian categories

Published online by Cambridge University Press:  29 July 2011

David Hébert
David Hébert*
Affiliation:
LAGA - UMR CNRS 7539, Institut Galilée - Université Paris 13, 99 avenue J.-B. Clément, 93430 Villetaneuse, France (email: hebert@math.univ-paris13.fr)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Bondarko defines and studies the notion of weight structure and he shows that there exists a weight structure over the category of Voevodsky motives with rational coefficients (over a field of characteristic 0). In this paper we extend this weight structure to the category of Beilinson motives (for any scheme of finite type over a base scheme which is excellent of dimension at most two) introduced and studied by Cisinsky and Déglise. We also check the weight exactness of the Grothendieck operations.

Keywords

weight structuresweight filtrationsChow motivesBeilinson motivesGrothendieck operations

MSC classification

Secondary: 14F42: Motivic cohomology; motivic homotopy theory 18A22: Special properties of functors (faithful, full, etc.) 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 5 , September 2011 , pp. 1447 - 1462
Copyright
Copyright © Foundation Compositio Mathematica 2011

References

[Ayo07]Ayoub, J., Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique (I–II), Astérisque, vol. 314–315 (Société Mathématique de France, Paris, 2007).Google Scholar
[BS01]Balmer, P. and Schlichting, M., Idempotent completion of triangulated categories, J. Algebra 236 (2001), 819–834.CrossRefGoogle Scholar
[BBD82]Beilinson, A., Bernstein, J. and Deligne, P., Faisceaux pervers, Astérisque, vol. 100 (Société Mathématique de France, Paris, 1982), 1–172.Google Scholar
[Bon10a]Bondarko, M., Weight for relative motives; relation with mixed sheaves (2010), arXiv:1007.4543v1 [math.AG].Google Scholar
[Bon10b]Bondarko, M., Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general), J. K-Theory 6 (2010), 387–504.CrossRefGoogle Scholar
[CD09]Cinsinski, D.-C. and Déglise, F., Triangulated categories of mixed motives (2009), arXiv:0912.2110v2 [math.AG].Google Scholar
[DG61]Dieudonné, J. and Grothendieck, A., Éléments de géométrie algébrique II, Publications Mathématiques de l’IHÉS, vol. 8 (Institut des Hautes Études Scientifiques, Bures-Sur-Yvette, France, 1961).Google Scholar
[H{é}b10]Hébert, D., Complexe de Poids, Dualité et Motifs de Beilinson (2010), arXiv:1010.5469v1 [math.AG].Google Scholar
[Lev08]Levine, M., Smooth motives (2008), arXiv:0807.2265v1 [math.AG].Google Scholar
[Nag63]Nagata, M., A generalization of the imbedding problem of an abstract variety in a complete variety, J. Math. Kyoto Univ. 3 (1963), 89–102.Google Scholar
[Nee01]Neeman, A., Triangulated categories, Annals of Mathematics Studies, vol. 148 (Princeton University Press, Princeton, NJ, 2001).CrossRefGoogle Scholar
[Pau08]Pauksztello, D., Compact corigid objects in triangulated categories and co-t-structures, Cent. Eur. J. Math. 6 (2008), 25–42.CrossRefGoogle Scholar
[VSF00]Voevodsky, V., Suslin, A. and Friedlander, E., Cycles, transfers and motivic homology theories, Annals of Mathematics Studies, vol. 143 (Princeton University Press, Princeton, NJ, 2000).Google Scholar