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1996 | 76 | 2 | 165-189
Tytuł artykułu

On large Picard groups and the Hasse Principle for curves and K3 surfaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
76
Numer
2
Strony
165-189
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-04-27
poprawiono
1995-10-26
Twórcy
autor
  • Université de Genève, Section de Mathématiques, 2-4, rue du Lièvre, CH-1211 Genève 24, Switzerland
  • École d'Ingénieurs, 4, rue de la Prairie, CH-1202 Genève, Switzerland
Bibliografia
  • [1] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math. 212 (1962), 7-25.
  • [2] A. Bremner, Algebraic points on quartic curves over function fields, Glasgow Math. J. 26 (1985), 187-190.
  • [3] A. Bremner, D. J. Lewis and P. Morton, Some varieties with points only in a field extension, Arch. Math. 43 (1984), 344-350.
  • [4] A. Brumer, Remarques sur les couples de formes quadratiques, C. R. Acad. Sci. Paris A 286 (1978), 679-681.
  • [5] J. W. S. Cassels, The arithmetic of certain quartic curves, Proc. Roy. Soc. Edinburgh 100 (1985), 201-218.
  • [6] J. W. S. Cassels, Local Fields, Cambridge Univ. Press, Cambridge, 1986.
  • [7] J. W. S. Cassels and A. Fröhlich (ed.), Algebraic Number Theory, Academic Press, London, 1967.
  • [8] J. W. S. Cassels and M. J. T. Guy, On the Hasse principle for cubic surfaces, Mathematika 13 (1966), 111-120.
  • [9] F. Châtelet, Variations sur un thème de Poincaré, Ann. Ecole Norm. Sup. 61 (1944), 249-300.
  • [10] J.-L. Colliot-Thélène, Les grands thèmes de François Châtelet, Enseign. Math. 34 (1988), 387-405.
  • [11] J.-L. Colliot-Thélène, D. Coray et J.-J. Sansuc, Descente et principe de Hasse pour certaines variétés rationnelles, J. Reine Angew. Math. 320 (1980), 150-191.
  • [12] J.-L. Colliot-Thélène et J.-J. Sansuc, La descente sur les variétés rationnelles, II, Duke Math. J. 54 (1987), 375-492.
  • [13] J.-L. Colliot-Thélène, J.-J. Sansuc and Sir P. Swinnerton-Dyer, Intersections of two quadrics and Châtelet surfaces, J. Reine Angew. Math. 373 (1987), 37-107; 374 (1987), 72-168.
  • [14] 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.
  • [15] J.-L. Colliot-Thélène and Sir P. Swinnerton-Dyer, Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties, J. Reine Angew. Math. 453 (1994), 49-112.
  • [16] D. Coray, Arithmetic on cubic surfaces, Ph.D. thesis, Trinity College, Cambridge, 1974, 66 pp.
  • [17] D. Coray, Algebraic points on cubic hypersurfaces, Acta Arith. 30 (1976), 267-296.
  • [18] D. Coray, On a problem of Pfister about intersections of three quadrics, Arch. Math. 34 (1980), 403-411.
  • [19] D. Coray, A remark on systems of quadratic forms, in: Math. Forschungsinstitut Oberwolfach, Tagungsbericht 22/1981: Quadratische Formen, 18.5-23.5.1981, 8-9.
  • [20] D. Coray and M. A. Tsfasman, Arithmetic on singular Del Pezzo surfaces, Proc. London Math. Soc. 57 (1988), 25-87.
  • [21] P. Deligne, Les conjectures de Weil, I, Publ. Math. I.H.E.S. 43 (1974), 273-307.
  • [22] W. Fulton, Intersection Theory, Springer, Berlin, 1984.
  • [23] A. Grothendieck, Le groupe de Brauer, III, Exemples et compléments, in: Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968.
  • [24] R. Hartshorne, Algebraic Geometry, Springer, New York, 1977.
  • [25] D. Husemöller, Elliptic Curves, Springer, New York, 1987.
  • [26] D. Kanevsky, Application of the conjecture on the Manin obstruction to various diophantine problems, Journées Arithmétiques de Besançon, Astérisque 147-148 (1987), 307-314.
  • [27] B. È. Kunyavskiĭ, A. N. Skorobogatov and M. A. Tsfasman, Del Pezzo surfaces of degree four, Suppl. Bull. Soc. Math. France 117 (2) (1989), Mémoire no. 37, 112 pp.
  • [28] S. Lang and A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819-827.
  • [29] S. Lichtenbaum, Duality theorems for curves over p-adic fields, Invent. Math. 7 (1969), 120-136.
  • [30] Yu. I. Manin, Cubic Forms, Nauka, Moscow, 1972 (in Russian); English transl.: North-Holland, Amsterdam, 1980.
  • [31] C. Manoil, Courbes sur une surface K3, thèse, Univ. Genève, 1992, 107 pp.
  • [32] A. S. Merkurjev and J.-P. Tignol, The multipliers of similitudes and the Brauer group of homogeneous varieties, preprint, Univ. Cath. Louvain, 1994, 30 pp.
  • [33] J. S. Milne, Étale Cohomology, Princeton Univ. Press, Princeton, N.J., 1980.
  • [34] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.
  • [35] D. Mumford, Lectures on Curves on an Algebraic Surface, Princeton Univ. Press, Princeton, N.J., 1966.
  • [36] P. Samuel, Anneaux factoriels, Inst. Pesq. Mat., Univ. S ao Paulo, 1963.
  • [37] P. Samuel, About Euclidean rings, J. Algebra 19 (1971), 282-301.
  • [38] J.-P. Serre, Corps locaux, Hermann, Paris, 1962.
  • [39] J.-P. Serre, Cours d'arithmétique, Presses Univ. France, Paris, 1970.
  • [40] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.
  • [41] T. A. Springer, Sur les formes quadratiques d'indice zéro, C. R. Acad. Sci. Paris 234 (1952), 1517-1519.
  • [42] T. A. Springer, Quadratic forms over fields with a discrete valuation, Indag. Math. 17 (1955), 352-362.
  • [43] V. E. Voskresenskiĭ, Algebraic Tori, Nauka, Moscow, 1977 (in Russian).
  • [44] E. Witt, Über ein Gegenbeispiel zum Normensatz, Math. Z. 39 (1935), 462-467.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav76i2p165bwm
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