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Méthode des fibrations et obstruction de Manin
David Harari
Source: Duke Math. J. Volume 75, Number 1
(1994), 221-260.
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Mathematical Reviews number (MathSciNet): MR1284820
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Digital Object Identifier: doi:10.1215/S0012-7094-94-07507-8
References
[1] J. W. S. Cassels and A. Fröhlich, Algebraic number theory, Proceedings of an instructional conference organized by the London Mathematical Society (a NATO Advanced Study Institute) with the support of the Inter national Mathematical Union. Edited by J. W. S. Cassels and A. Fröhlich, Academic Press, London, 1967.
Mathematical Reviews (MathSciNet): MR35:6500
Zentralblatt MATH: 0153.07403
[2] J.-L. Colliot-Thelene, Surfaces rationnelles fibrées en coniques de degré $4$, Séminaire de Théorie des Nombres, Paris 1988–1989 ed. C. Goldstein, Progr. Math., vol. 91, Birkhäuser Boston, Boston, MA, 1990, pp. 43–55.
Mathematical Reviews (MathSciNet): MR92j:14027
Zentralblatt MATH: 0731.14033
[3] J.-L. Colliot-Thélène, L'arithmétique des variétés rationnelles, Ann. Fac. Sci. Toulouse Math. (6) 1 (1992), no. 3, 295–336.
Mathematical Reviews (MathSciNet): MR94i:11040
Zentralblatt MATH: 0787.14012
[4] J.-L. Colliot-Thélène, D. Coray, and J.-J. Sansuc, Descente et principe de Hasse pour certaines variétés rationnelles, J. Reine Angew. Math. 320 (1980), 150–191.
Mathematical Reviews (MathSciNet): MR82f:14020
Zentralblatt MATH: 0434.14019
[5] J.-L. Colliot-Thélène, D. Kanevsky, and J.-J. Sansuc, Arithmétique des surfaces cubiques diagonales, Diophantine approximation and transcendence theory (Bonn, 1985), Lecture Notes in Math., vol. 1290, Springer-Verlag, Berlin, 1987, pp. 1–108.
Mathematical Reviews (MathSciNet): MR89g:11051
Zentralblatt MATH: 0639.14018
[6] J.-L. Colliot-Thélène and M. Ojanguren, Variétés unirationnelles non rationnelles: au-delà de l'exemple d'Artin et Mumford, Invent. Math. 97 (1989), no. 1, 141–158.
Mathematical Reviews (MathSciNet): MR90m:14012
Zentralblatt MATH: 0686.14050
Digital Object Identifier: doi:10.1007/BF01850658
[7] J.-L. Colliot-Thélène and W. Raskind, $\scr K\sb 2$-cohomology and the second Chow group, Math. Ann. 270 (1985), no. 2, 165–199.
Mathematical Reviews (MathSciNet): MR86m:14005
Zentralblatt MATH: 0536.14004
Digital Object Identifier: doi:10.1007/BF01456181
[8] J.-L. Colliot-Thélène and 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), no. 2, 221–245.
Mathematical Reviews (MathSciNet): MR92j:14009
Zentralblatt MATH: 0752.14004
Digital Object Identifier: doi:10.1007/BF01232266
[9] J.-L. Colliot-Thélène and P. Salberger, Arithmetic on some singular cubic hypersurfaces, Proc. London Math. Soc. (3) 58 (1989), no. 3, 519–549.
Mathematical Reviews (MathSciNet): MR90e:11091
Zentralblatt MATH: 0638.14011
Digital Object Identifier: doi:10.1112/plms/s3-58.3.519
[10]1 J.-L. Colliot-Thélène and J.-J. Sansuc, Torseurs sous des groupes de type multiplicatif; applications à l'étude des points rationnels de certaines variétés algébriques, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 18, Aii, A1113–A1116.
Mathematical Reviews (MathSciNet): MR54:2657
Zentralblatt MATH: 0337.14014
[10]2 J.-L. Colliot-Thélène and J.-J. Sansuc, Variétés de première descente attachées aux variétés rationnelles, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 16, A967–A970.
Mathematical Reviews (MathSciNet): MR56:5561
Zentralblatt MATH: 0349.14026
[10]3 J.-L. Colliot-Thélène and J.-J. Sansuc, La descente sur une variété rationnelle définie sur un corps de nombres, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 19, A1215–A1218.
Mathematical Reviews (MathSciNet): MR56:5565
Zentralblatt MATH: 0349.14015
[11] J.-L. Colliot-Thélène and J.-J. Sansuc, La descente sur les variétés rationnelles. II, Duke Math. J. 54 (1987), no. 2, 375–492.
Mathematical Reviews (MathSciNet): MR89f:11082
Zentralblatt MATH: 0659.14028
Digital Object Identifier: doi:10.1215/S0012-7094-87-05420-2
Project Euclid: euclid.dmj/1077305668
[12]1 J.-L. Colliot-Thélène, J.-J. Sansuc, and Peter Swinnerton-Dyer, Intersections of two quadrics and Châtelet surfaces. I, J. Reine Angew. Math. 373 (1987), 37–107.
Mathematical Reviews (MathSciNet): MR88m:11045a
Zentralblatt MATH: 0622.14029
[12]2 J.-L. Colliot-Thélène, J.-J. Sansuc, and Peter Swinnerton-Dyer, Intersections of two quadrics and Châtelet surfaces. II, J. Reine Angew. Math. 374 (1987), 72–168.
Mathematical Reviews (MathSciNet): MR88m:11045b
Zentralblatt MATH: 0622.14030
[13] J.-L. Colliot-Thélène and A. N. Skorobogatov, Approximation faible pour les intersections de deux quadriques en dimension $3$, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 2, 127–132.
Mathematical Reviews (MathSciNet): MR93c:11045
Zentralblatt MATH: 0757.14028
[14] D. Coray and M. A. Tsfasman, Arithmetic on singular Del Pezzo surfaces, Proc. London Math. Soc. (3) 57 (1988), no. 1, 25–87.
Mathematical Reviews (MathSciNet): MR89f:11083
Zentralblatt MATH: 0653.14018
Digital Object Identifier: doi:10.1112/plms/s3-57.1.25
[15] D. Coray, Two remarks on the Bertini theorems, non publié, 1980.
[16] A. Debbache, Principe de Hasse pour certaines intersections de deux quadriques, prépublication, 1990.
[17] T. Ekedahl, An effective version of Hilbert's irreducibility theorem, Séminaire de Théorie des Nombres, Paris 1988–1989 ed. C. Goldstein, Progr. Math., vol. 91, Birkhäuser Boston, Boston, MA, 1990, pp. 241–249.
Mathematical Reviews (MathSciNet): MR92f:14018
Zentralblatt MATH: 0729.12005
[18] W. Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85k:14004
Zentralblatt MATH: 0541.14005
[19] W. Fulton and R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Algebraic geometry (Chicago, Ill., 1980), Lecture Notes in Math., vol. 862, Springer, Berlin, 1981, pp. 26–92.
Mathematical Reviews (MathSciNet): MR83i:14002
Zentralblatt MATH: 0484.14005
[20] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978.
Mathematical Reviews (MathSciNet): MR80b:14001
Zentralblatt MATH: 0408.14001
[21] A. Grothendieck, Géométrie algébrique et géométrie formelle, exposé Bourbaki (1958/1959), vol. 182, Secrétariat Mathématique, Paris, 1962, reproduit dans Fondements de la géométrie algébrique.
Zentralblatt MATH: 0229.14005
Mathematical Reviews (MathSciNet): MR146040
[22] A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. III, Inst. Hautes Études Sci. Publ. Math. (1966), no. 28, 255.
Mathematical Reviews (MathSciNet): MR36:178
Zentralblatt MATH: 0144.19904
[23] A. Grothendieck and M. Demazure, Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 152, Springer-Verlag, Berlin, 1962/1964.
Mathematical Reviews (MathSciNet): MR43:223b
Zentralblatt MATH: 0209.24201
[24] A. Grothendieck, Le groupe de Brauer. II. Théorie cohomologique, Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam,Masson, 1968, pp. 67–87.
Mathematical Reviews (MathSciNet): MR39:5586b
Zentralblatt MATH: 0198.25803
[25] A. Grothendieck, Le groupe de Brauer. III. Exemples et compléments, Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, 1968, pp. 88–188.
Mathematical Reviews (MathSciNet): MR39:5586c
Zentralblatt MATH: 0198.25901
[26] D. Harari, Groupe de Brauer de certaines hypersurfaces, Astérisque (1992), no. 209, 14, 203–214, dans Journées arithmétiques de Genève 1991.
Mathematical Reviews (MathSciNet): MR94a:11094
Zentralblatt MATH: 0795.14023
[27] D. Harari, Principe de Hasse et approximation faible sur certaines hypersurfaces, prépublication, 1993.
[28] R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977.
Mathematical Reviews (MathSciNet): MR57:3116
Zentralblatt MATH: 0367.14001
[29] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326.
Mathematical Reviews (MathSciNet): MR33:7333
Zentralblatt MATH: 0122.38603
Digital Object Identifier: doi:10.2307/1970547
JSTOR: links.jstor.org
[30] D. Kanevsky, Application of the conjecture on the Manin obstruction to various Diophantine problems, Astérisque (1987), no. 147-148, 307–314, 345, dans Journées arithmétiques de Besançon, 1985.
Mathematical Reviews (MathSciNet): MR89b:11032
Zentralblatt MATH: 0625.14010
[31] S. Lang, Algebraic Number Theory, Springer-Verlag, New York, 1986.
Zentralblatt MATH: 0601.12001
Mathematical Reviews (MathSciNet): MR1282723
[32] S. Lang, Fundamentals of Diophantine geometry, Springer-Verlag, New York, 1983.
Mathematical Reviews (MathSciNet): MR85j:11005
Zentralblatt MATH: 0528.14013
[33] S. Lang and A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819–827.
Mathematical Reviews (MathSciNet): MR16,398d
Zentralblatt MATH: 0058.27202
Digital Object Identifier: doi:10.2307/2372655
JSTOR: links.jstor.org
[34] Yu. I. Manin, Le groupe de Brauer-Grothendieck en géométrie diophantienne, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, pp. 401–411.
Mathematical Reviews (MathSciNet): MR55:356
Zentralblatt MATH: 0239.14010
[35] Yu. I. Manin and M. Hazewinkel, Cubic forms: algebra, geometry, arithmetic, North-Holland Publishing Co., Amsterdam, 1974.
Mathematical Reviews (MathSciNet): MR57:343
Zentralblatt MATH: 0277.14014
[36] H. Matsumura, Commutative algebra, Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980.
Mathematical Reviews (MathSciNet): MR82i:13003
Zentralblatt MATH: 0441.13001
[37] J.-S. Milne, Étale cohomology, Princeton Mathematical Series, vol. 33, Princeton University Press, Princeton, N.J., 1980.
Mathematical Reviews (MathSciNet): MR81j:14002
Zentralblatt MATH: 0433.14012
[38] Y. Morita, A note on the Hilbert irreducibility theorem. The irreducibility theorem and the strong approximation theorem, Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 4, 101–104.
Mathematical Reviews (MathSciNet): MR91j:11089
Zentralblatt MATH: 0725.12003
Digital Object Identifier: doi:10.3792/pjaa.66.101
Project Euclid: euclid.pja/1195512542
[39] H. Nishimura, Some remarks on rational points, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 29 (1955), 189–192.
Mathematical Reviews (MathSciNet): MR20:2349
Zentralblatt MATH: 0068.14802
[40] D. Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, No. 5, Published for the Tata Institute of Fundamental Research, Bombay, 1970.
Mathematical Reviews (MathSciNet): MR44:219
Zentralblatt MATH: 0223.14022
[41] P. Salberger and A. N. Skorobogatov, Weak approximation for surfaces defined by two quadratic forms, Duke Math. J. 63 (1991), no. 2, 517–536.
Mathematical Reviews (MathSciNet): MR93e:11079
Zentralblatt MATH: 0770.14019
Digital Object Identifier: doi:10.1215/S0012-7094-91-06322-2
Project Euclid: euclid.dmj/1077295932
[42] J.-J. Sansuc, Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres, J. Reine Angew. Math. 327 (1981), 12–80.
Mathematical Reviews (MathSciNet): MR83d:12010
Zentralblatt MATH: 0468.14007
Digital Object Identifier: doi:10.1515/crll.1981.327.12
[43] P. Schneider, Über gewisse Galoiscohomologiegruppen, Math. Z. 168 (1979), no. 2, 181–205.
Mathematical Reviews (MathSciNet): MR81i:12010
Zentralblatt MATH: 0421.12024
Digital Object Identifier: doi:10.1007/BF01214195
[44] J.-P. Serre, Corps locaux, Hermann, Paris, 1968.
Mathematical Reviews (MathSciNet): MR50:7096
[45] J.-P. Serre, Cours d'arithmétique, Collection SUP: “Le Mathématicien”, vol. 2, Presses Universitaires de France, Paris, 1970.
Mathematical Reviews (MathSciNet): MR41:138
Zentralblatt MATH: 0225.12002
[46] J.-P. Serre, Spécialisation des éléments de $\rm Br\sb 2(\bf Q(T\sb 1,\cdots,T\sb n))$, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 7, 397–402.
Mathematical Reviews (MathSciNet): MR91m:12007
Zentralblatt MATH: 0711.13002
[47] A. N. Skorobogatov, Arithmetic on certain quadric bundles of relative dimension $2$. I, J. Reine Angew. Math. 407 (1990), 57–74.
Mathematical Reviews (MathSciNet): MR91j:14024
Zentralblatt MATH: 0692.14001
Digital Object Identifier: doi:10.1515/crll.1990.407.57
[48] A. N. Skorobogatov, On the fibration method for proving the Hasse principle and weak approximation, Séminaire de Théorie des Nombres, Paris 1988–1989 ed. C. Goldstein, Progr. Math., vol. 91, Birkhäuser Boston, Boston, MA, 1990, avec B. Kunyavskiî pour l'appendice, pp. 205–219.
Mathematical Reviews (MathSciNet): MR92i:11064
Zentralblatt MATH: 0748.14002
[49] V. E. Voskresenskii, Algebraicheskie tory, Izdat. “Nauka”, Moscow, 1977, en russe.
Mathematical Reviews (MathSciNet): MR58:22078
Zentralblatt MATH: 0499.14013
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