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1997 | 79 | 2 | 113-135
Tytuł artykułu

Double fibres and double covers: paucity of rational points

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
79
Numer
2
Strony
113-135
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-28
Twórcy
  • C.N.R.S., URA D0752, Mathématiques, Bâtiment 425, Université de Paris-Sud, F-91405 Orsay, France
  • Institute for Problems of Information Transmission, Russian Academy of Sciences, 19, Bolshoi Karetnyi, Moscow 101447, Russia
  • Laboratoire de mathématiques discrètes, C.N.R.S., UPR 9016, Equipe "Arithmétique et théorie de l'information", Luminy Case 930, F-13288 Marseille Cédex 9, France
  • Isaac Newton Institute, 20 Clarkson Road, Cambridge CB3 0EH, Great Britain
Bibliografia
  • [A] D. Abramovich, Lang maps and Harris's conjecture, Israel J. Math., to appear.
  • [BPV] W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Ergeb. Math. Grenzgeb. (3) 4, Springer, 1984.
  • [B] A. Beauville, Surfaces algébriques complexes, Astérisque 54 (1978).
  • [Ca.1] J. W. S. Cassels, The rational solutions of the diophantine equation Y²=X³-D, Acta Math. 82 (1950), 243-273.
  • [Ca.2] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193-291.
  • [CT/S.1] J.-L. Colliot-Thélène et J.-J. Sansuc, La descente sur les variétés rationnelles, in: Journées de géométrie algébrique d'Angers, A. Beauville (éd.), Sijthoff and Noordhoff, Alphen aan den Rijn, 1980, 223-237.
  • [CT/S.2] J.-L. Colliot-Thélène et J.-J. Sansuc, La descente sur les variétés rationnelles, II, Duke Math. J. 54 (1987), 375-492.
  • [CT/Sk/SwD.1] J.-L. Colliot-Thélène, A. N. Skorobogatov and Sir Peter Swinnerton-Dyer, Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points, in preparation.
  • [CT/Sk/SwD.2] J.-L. Colliot-Thélène, A. N. Skorobogatov and Sir Peter Swinnerton-Dyer, Rational points and zero-cycles on fibred varieties: Schinzel's hypothesis and Salberger's device, in preparation.
  • [CT/SwD] J.-L. Colliot-Thélène and Sir Peter Swinnerton-Dyer, Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties, J. Reine Angew. Math. 453 (1994), 49-112.
  • [F] G. Faltings, Complements to Mordell, in: Rational Points, Seminar Bonn/Wuppertal 1983/1984, G. Faltings, G. Wüstholz et al. (eds.), Aspekte der Math. E6, Vieweg, 1984, 203-227.
  • [K] A. W. Knapp, Elliptic Curves, Princeton University Press, 1992.
  • [MD] M. Martin-Deschamps, La construction de Kodaira-Parshin, Astérisque 127 (1985), 256-272.
  • [Maz.1] B. Mazur, The topology of rational points, Experiment. Math. 1 (1992), 35-45.
  • [Maz.2] B. Mazur, Speculations about the topology of rational points: an up-date, Astérisque 228 (1995), 165-181.
  • [R] D. E. Rohrlich, Variation of the root number in families of elliptic curves, Compositio Math. 87 (1993), 119-151.
  • [Sh] I. R. Shafarevich et al., Algebraic surfaces, Proc. Steklov Inst. Math. 75 (1967).
  • [S] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, 1986.
  • [Sk] A. N. Skorobogatov, Descent on fibrations over the projective line, Amer. J. Math. 118 (1996), 905-923.
  • [SwD] Sir Peter Swinnerton-Dyer, Rational points on certain intersections of two quadrics, in: Abelian Varieties, Proc. Conf. Egloffstein, W. Barth, K. Hulek and H. Lange (eds.), de Gruyter, Berlin, 1995, 273-292.
  • [W.1] A. Weil, Arithmétique et géométrie sur les variétés algébriques, in: Actualités Sci. Indust. 206, Hermann, Paris, 1935, 3-16; reprinted in: Oeuvres Scientifiques, Vol. I, Springer, 1980, 87-100.
  • [W.2] A. Weil, Arithmetic on algebraic varieties, Ann. of Math. 53 (1951), 412-444.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav79i2p113bwm
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