L'arithmétique du groupe de Chow des zéro-cycles
Journal de Théorie des Nombres de Bordeaux, Volume 7 (1995) no. 1, pp. 51-73. 
@article{JTNB_1995__7_1_51_0,
     author = {Jean-Louis Colliot-Th\'el\`ene},
     title = {L'arithm\'etique du groupe de {Chow} des z\'ero-cycles},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {51--73},
     publisher = {Universit\'e Bordeaux I},
     volume = {7},
     number = {1},
     year = {1995},
     doi = {10.5802/jtnb.130},
     zbl = {0870.14002},
     mrnumber = {1413566},
     language = {fr},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.130/}
}
TY  - JOUR
TI  - L'arithmétique du groupe de Chow des zéro-cycles
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 1995
DA  - 1995///
SP  - 51
EP  - 73
VL  - 7
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.130/
UR  - https://zbmath.org/?q=an%3A0870.14002
UR  - https://www.ams.org/mathscinet-getitem?mr=1413566
UR  - https://doi.org/10.5802/jtnb.130
DO  - 10.5802/jtnb.130
LA  - fr
ID  - JTNB_1995__7_1_51_0
ER  - 
%0 Journal Article
%T L'arithmétique du groupe de Chow des zéro-cycles
%J Journal de Théorie des Nombres de Bordeaux
%D 1995
%P 51-73
%V 7
%N 1
%I Université Bordeaux I
%U https://doi.org/10.5802/jtnb.130
%R 10.5802/jtnb.130
%G fr
%F JTNB_1995__7_1_51_0
Jean-Louis Colliot-Thélène. L'arithmétique du groupe de Chow des zéro-cycles. Journal de Théorie des Nombres de Bordeaux, Volume 7 (1995) no. 1, pp. 51-73. doi : 10.5802/jtnb.130. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.130/

[1] S. Bloch, Torsion algebraic cycles, K2 and Brauer groups of function fields, in L.N.M. 844 (éd. M. Kervaire et M. Ojanguren) Springer 1981. | Zbl: 0467.12011

[2] S. Bloch, On the Chow groups of certain rational surfaces, Ann. Sci. Ec. Norm. Sup. 14 (1981), 41-59. | Numdam | MR: 618730 | Zbl: 0524.14006

[3] S. Bloch, Algebraic K-theory, motives and algebraic cycles, Proceedings of the ICM, Kyoto, Japan 1990, Springer 1991, Vol. 1, 43-54. | MR: 1159204 | Zbl: 0759.14001

[4] S. Bloch and A. Ogus, Gersten's conjecture and the homology of schemes, Ann. Sci. Éc. Norm. Sup. 7 (1974), 181-202. | Numdam | MR: 412191 | Zbl: 0307.14008

[5] S. Bloch and V. Srinivas, Remarks on correspondences and algebraic cycles, Am. J. Math. 105 (1983), 1235-1253. | MR: 714776 | Zbl: 0525.14003

[6] J.W.S. Cassels, Arithmetic on curves of genus 1 (VII). The dual exact sequence, J. für die reine und angew. Math. (Crelle) 216 (1964), 150-158. | MR: 169849 | Zbl: 0146.42304

[7] J.-L. Colliot-Thélène, Hilbert's theorem 90 for K2, with application to the Chow groups of rational surfaces, Invent. math. 71 (1983), 1-20. | MR: 688259 | Zbl: 0527.14011

[8] J.-L. Colliot-Thélène, Cycles algébriques de torsion et K-théorie algébrique, in Arithmetical Algebraic Geometry, C.I.M.E. 1991, E. Ballico ed., L. N. M. 1553, Springer-Verlag, 1993. | MR: 1338859 | Zbl: 0806.14002

[9] J.-L. Colliot-Thélène et F. Ischebeck, L'équivalence, rationnelle sur les cycles de dimension zéro des variétés algébriques réelles, C. R. Acad. Sc. Paris 292 (1981), 723-725. | MR: 618896 | Zbl: 0472.14016

[10] J.-L. Colliot-Thélène et W. Raskind, Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: un théorème de finitude pour la torsion, Invent. math. 105 (1991), 221-245. | MR: 1115542 | Zbl: 0752.14004

[11] J.-L. Colliot-Thélène et J.-J. Sansuc, La R-équivalence sur les tores, Ann. Sci. Éc. Norm. Sup. 10 (1977), 175-229. | Numdam | MR: 450280 | Zbl: 0356.14007

[12] J.-L. Colliot-Thélène and J.-J. Sansuc, On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch, Duke Math. J. 48 (1981), 421-447. | MR: 620258 | Zbl: 0479.14006

[13] J.-L. Colliot-Thélène et J.-J. Sansuc, La descente sur les variétés rationnelles, II, Duke Math. J. 54 (1987), 375-492. | MR: 899402 | Zbl: 0659.14028

[14] J.-L. Colliot-Thélène, J.-J. Sansuc et C. Soulé, Torsion dans le groupe de Chow de codimension deux, Duke Math. J. 50 (1983), 763-801. | MR: 714830 | Zbl: 0574.14004

[15] J.-L. Colliot-Thélène, J.-J. Sansuc and Sir Peter Swinnerton-Dyer, Intersections of two quadrics and Châtelet surfaces, I, J. für die reine und angew. Math. (Crelle) 373 (1987) 37-107; II, ibid. 374 (1987) 72-168. | MR: 870307 | Zbl: 0622.14029

[16] J.-L. Colliot-Thélène and C. Scheiderer, Zero-cycles and cohomology on real algebraic varieties, à paraître dans Topology. | MR: 1380515 | Zbl: 0882.14016

[17] J.-L. Colliot-Thélène et A.N. Skorobogatov, Groupe de Chow des zéro-cycles sur les fibrés en quadriques, K-Theory 7 (1993), 477-500. | MR: 1255062 | Zbl: 0837.14002

[18] J.-L. Colliot-Thélène and Sir Peter Swinnerton-Dyer, Hasse principle and weak approximation for pencils of Severi-Brauer varieties and similar varieties, Journal für die reine und angew. Math. (Crelle) 453 (1994), 49-112. | MR: 1285781 | Zbl: 0805.14010

[19] C.S. Dalawat, Groupe des classes de zéro-cycles sur les surfaces rationnelles définies sur un corps local, Thèse, Université de Paris-Sud, Juin 1993.

[20] M. Flach, A finiteness theorem for the symmetric square of an elliptic curve, Invent. math. 109 (1992), 307-327. | MR: 1172693 | Zbl: 0781.14022

[21] W. Fulton, Intersection Theory, Ergeb. der Math. und ihrer Grenzgeb. Bd. 2, Springer-Verlag, Berlin, 1984. | MR: 732620 | Zbl: 0541.14005

[22] Ph. Gille, Un théorème de finitude arithmétique sur les groupes réductifs, C. R. Acad. Sc. Paris 316 (1993), 701-704. | MR: 1214419 | Zbl: 0806.20036

[23] D. Harari, Méthode des fibrations et obstruction de Manin, Duke Math. J. 75 (1994), 221-260. | MR: 1284820 | Zbl: 0847.14001

[24] K. Kato and S. Saito, Global class field theory of arithmetic schemes, Contemp. Math. 55, vol. 1, 255-331. | MR: 862639 | Zbl: 0614.14001

[25] A. Langer and S. Saito, Torsion zero-cycles on the self-product of a modular elliptic curve, preprint 1994.

[26] S. Lichtenbaum, Duality theorems for curves over p-adic fields, Invent. math. 7 (1969),120-136. | MR: 242831 | Zbl: 0186.26402

[27] Yu. I. Manin, Le groupe de Brauer-Grothendieck en géométrie diophantienne, in Actes Congrès intern. math. Nice, 1970, Tome I, 401-411. | MR: 427322 | Zbl: 0239.14010

[28] A.S. Merkur'Ev and A.A. Suslin, K-cohomology of Severi-Brauer varieties and norm residue homomorphism, Izv. Akad. Nauk SSSR 46 (1982) 1011-1146 = Math. USSR Izv. 21 (1983) 307-341. | MR: 675529 | Zbl: 0525.18008

[29] S.J. Mildenhall, Cycles in a product of elliptic curves, and a group analogous to the class group, Duke Math. J. 67 (1992), 387-406. | MR: 1177312 | Zbl: 0788.14004

[30] J.S. Milne, Arithmetic Duality Theorems, Perspectives in Math. vol. 1, Academic Press 1986. | MR: 881804 | Zbl: 0613.14019

[31] R. Parimala and V. Suresh, Zero-cycles on quadric fibrations: Finiteness theorems and the cycle map, Invent. Math. 122 (1995), 83-117. | MR: 1354955 | Zbl: 0865.14002

[32] W. Raskind, Torsion algebraic cycles on varieties over local fields, in Algebraic K-theory: Connections with Geometry and Topology, Lake Louise 1987, J.F. Jardine and V.P. Snaith ed., Kluwer Academic Publishers 1989. | MR: 1045854 | Zbl: 0709.14005

[33] S. Saito, Some observations on motivic cohomology of arithmetic schemes, Invent. math. 98 (1989), 371-404. | MR: 1016270 | Zbl: 0694.14005

[34] S. Saito, Cycle map on torsion algebraic cycles of codimension two, Invent. math. 106 (1991), 443-460. | MR: 1134479 | Zbl: 0764.14004

[35] S. Saito and R. Sujatha, A finiteness theorem for cohomology of surfaces over p-adic fields and an application to Witt groups, in Algebraic K-Theory, Quadratic Forms and Central Simple Algebras, 1992 A. M. S. Summer Conference (Santa Barbara), B. Jacob and A. Rosenberg ed., Proc. Symposia in Pure Mathematics, Vol. 58, Part 2, 403-416. | MR: 1327311 | Zbl: 0820.14013

[36] P. Salberger, K-theory of orders and their Brauer-Severi schemes, Thèse, Université de Göteborg, 1985.

[37] P. Salberger, Galois descent and class groups of orders, in Orders and their applications, Oberwolfach 1984, I. Reiner and R. W. Roggenkamp ed., L. N. M. 1142, Springer-Verlag, 1985. | MR: 812503 | Zbl: 0579.16002

[38] P. Salberger, Zero-cycles on rational surfaces over number fields, Invent. math. 91 (1988),505-524. | MR: 928495 | Zbl: 0688.14008

[39] P. Salberger, Chow groups of codimension two and l-adic realizations of motivic cohomology, in Séminaire de théorie des nombres, Paris 1991/1992, éd. Sinnou David, Progress in Mathematics 116 (1993), 247-277. | MR: 1300892 | Zbl: 0833.14004

[40] J.-J. Sansuc, A propos d'une conjecture arithmétique sur le groupe de Chow d'une surface rationnelle, Séminaire de théorie des nombres, Bordeaux 1981/1982, exp. 33. | MR: 695346 | Zbl: 0538.14002

[41] H. Shen, Monodromy and torsion algebraic cycles, Thèse, Arizona State University, Juillet 1993.

Cited by Sources: