Double fibres and double covers: paucity of rational points

J.-L. Colliot-Thélène; A. N. Skorobogatov; Sir Peter Swinnerton-Dyer

Acta Arithmetica (1997)

  • Volume: 79, Issue: 2, page 113-135
  • ISSN: 0065-1036

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J.-L. Colliot-Thélène, A. N. Skorobogatov, and Sir Peter Swinnerton-Dyer. "Double fibres and double covers: paucity of rational points." Acta Arithmetica 79.2 (1997): 113-135. <http://eudml.org/doc/206971>.

@article{J1997,
author = {J.-L. Colliot-Thélène, A. N. Skorobogatov, Sir Peter Swinnerton-Dyer},
journal = {Acta Arithmetica},
keywords = {double fibres; double covers; density of rational points; Mordell conjecture; hyperelliptic surface},
language = {eng},
number = {2},
pages = {113-135},
title = {Double fibres and double covers: paucity of rational points},
url = {http://eudml.org/doc/206971},
volume = {79},
year = {1997},
}

TY - JOUR
AU - J.-L. Colliot-Thélène
AU - A. N. Skorobogatov
AU - Sir Peter Swinnerton-Dyer
TI - Double fibres and double covers: paucity of rational points
JO - Acta Arithmetica
PY - 1997
VL - 79
IS - 2
SP - 113
EP - 135
LA - eng
KW - double fibres; double covers; density of rational points; Mordell conjecture; hyperelliptic surface
UR - http://eudml.org/doc/206971
ER -

References

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  2. [BPV] W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Ergeb. Math. Grenzgeb. (3) 4, Springer, 1984. Zbl0718.14023
  3. [B] A. Beauville, Surfaces algébriques complexes, Astérisque 54 (1978). 
  4. [Ca.1] J. W. S. Cassels, The rational solutions of the diophantine equation Y²=X³-D, Acta Math. 82 (1950), 243-273. 
  5. [Ca.2] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193-291. 
  6. [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. Zbl0451.14018
  7. [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. Zbl0659.14028
  8. [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. 
  9. [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. 
  10. [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. Zbl0805.14010
  11. [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. 
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  16. [R] D. E. Rohrlich, Variation of the root number in families of elliptic curves, Compositio Math. 87 (1993), 119-151. Zbl0791.11026
  17. [Sh] I. R. Shafarevich et al., Algebraic surfaces, Proc. Steklov Inst. Math. 75 (1967). 
  18. [S] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, 1986. 
  19. [Sk] A. N. Skorobogatov, Descent on fibrations over the projective line, Amer. J. Math. 118 (1996), 905-923. Zbl0880.14008
  20. [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. Zbl0849.14009
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  22. [W.2] A. Weil, Arithmetic on algebraic varieties, Ann. of Math. 53 (1951), 412-444. Zbl0043.27002

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