Algèbre homologique
f-catégories, tours et motifs de Tate
[f-categories, towers, and Tate motives]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1337-1342.

The aim of this Note is to give a simple proof of the following fact: the triangulated category of Tate motives over a field k is equivalent to the bounded derived category of its heart, provided that k is algebraic over Q (Theorem 1.3).

Le but de cette Note est de donner une preuve simple de l'énoncé suivant : sur un corps algébrique sur Q, la catégorie triangulée des motifs de Tate est équivalente à la catégorie dérivée bornée de son coeur (Théorème 1.3).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.10.016
Wildeshaus, Jörg 1

1 LAGA, UMR 7539, Institut Galilée, université Paris 13, avenue Jean-Baptiste-Clément, 93430 Villetaneuse, France
@article{CRMATH_2009__347_23-24_1337_0,
     author = {Wildeshaus, J\"org},
     title = {\protect\emph{f}-cat\'egories, tours et motifs de {Tate}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1337--1342},
     publisher = {Elsevier},
     volume = {347},
     number = {23-24},
     year = {2009},
     doi = {10.1016/j.crma.2009.10.016},
     language = {fr},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.016/}
}
TY  - JOUR
AU  - Wildeshaus, Jörg
TI  - f-catégories, tours et motifs de Tate
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1337
EP  - 1342
VL  - 347
IS  - 23-24
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2009.10.016/
DO  - 10.1016/j.crma.2009.10.016
LA  - fr
ID  - CRMATH_2009__347_23-24_1337_0
ER  - 
%0 Journal Article
%A Wildeshaus, Jörg
%T f-catégories, tours et motifs de Tate
%J Comptes Rendus. Mathématique
%D 2009
%P 1337-1342
%V 347
%N 23-24
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2009.10.016/
%R 10.1016/j.crma.2009.10.016
%G fr
%F CRMATH_2009__347_23-24_1337_0
Wildeshaus, Jörg. f-catégories, tours et motifs de Tate. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1337-1342. doi : 10.1016/j.crma.2009.10.016. http://www.numdam.org/articles/10.1016/j.crma.2009.10.016/

[1] André, Y. Une introduction aux motifs, Panoramas et Synthèses, vol. 17, Soc. Math. France, 2004

[2] Beilinson, A.A.; Bernstein, J.; Deligne, P. Faisceaux pervers, Astérisque, Volume 100 (1982)

[3] Beilinson, A.A. On the derived category of perverse sheaves (Manin, Yu.I., ed.), K-Theory, Arithmetic and Geometry, Lect. Notes Math., vol. 1289, Springer-Verlag, 1987, pp. 27-41

[4] Bloch, S. Algebraic cycles and algebraic K-theory, Adv. in Math., Volume 61 (1986), pp. 267-304

[5] Bloch, S. The moving lemma for higher Chow groups, J. Algebraic Geom., Volume 3 (1994), pp. 537-568

[6] Buchsbaum, A. Satellites and exact functors, Ann. of Math., Volume 71 (1960), pp. 199-209

[7] Deligne, P.; Goncharov, A.B. Groupes fondamentaux motiviques de Tate mixte, Ann. Scient. ENS, Volume 38 (2005), pp. 1-56

[8] Keller, B.; Vossieck, D. Sous les catégories dérivées, C. R. Acad. Sci., Volume 305 (1987), pp. 225-228

[9] Keller, B. Derived categories and universal problems, Comm. Algebra, Volume 19 (1991), pp. 699-747

[10] Levine, M. Tate motives and the vanishing conjectures for algebraic K-theory, Proceedings of the NATO Advanced Study Institute, held at Lake Louise, Alberta, December 12–16, 1991 (Goerss, P.G.; Jardine, J.F., eds.) (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.), Volume vol. 407, Kluwer (1993), pp. 167-188

[11] Levine, M. Mixed motives (Friedlander, E.M.; Grayson, D.R., eds.), Handbook of K-Theory, Springer, 2005, pp. 429-521

[12] Voevodsky, V. Triangulated categories of motives, Ann. of Math. Studies, vol. 143, Princeton Univ. Press, 2000 (in: V. Voevodsky, A. Suslin, E.M. Friedlander, Cycles, Transfers, and Motivic Homology Theories Chapter 5)

Cited by Sources: