Skip to main content
Log in

Modèles minimaux des variétés abéliennes sur les corps locaux et globaux

  • Published:
Publications Mathématiques de l'Institut des Hautes Études Scientifiques Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliographie

  1. N. Bourbaki,Éléments de mathématique, liv. II(Algèbre), chap. VII, Actualités sc. et indust., no 1179, Paris, Hermann, 1952.

    Google Scholar 

  2. W. L. Chow, Projective embedding of homogeneous spaces,Lefschetz Conference Volume, Princeton University Press, 1957.

  3. J. Dieudonné etA. Grothendieck, Éléments de géométrie algébrique, I,Publ. Math. Inst. Htes Ét. scientifiques, Paris,4, 1960.

  4. M. Greenberg,Pro-algebraic structure on the rational subgroup of a p-adic abelian variety, Thesis, Princeton Univ., 1959.

  5. M. Greenberg, Schemata over local rings,Ann. Math., 73 (1961), pp. 624–648.

    Article  Google Scholar 

  6. J. Igusa, Fibre systems of jacobian varieties,Amer. J. Math., vol. 78 (1956), pp. 171–199 et 745–760.

    Article  MathSciNet  Google Scholar 

  7. K. Kodaira, On compact analytic surfaces,Princeton Math. Series, 24, pp. 121–135.

  8. S. Koizumi, On specialization of the Albanese and Picard varieties,Mem. Coll. Sci. Univ. Kyoto, 32 (1960), pp. 371–382.

    MATH  MathSciNet  Google Scholar 

  9. S. Koizumi andG. Shimura, On specialization of abelian varieties,Scientific Papers of the College of General Education University of Tokyo, 9 (1959), pp. 187–211.

    MATH  MathSciNet  Google Scholar 

  10. S. Lang,Abelian varieties, Interscience Tracts, New York, 1959.

    Google Scholar 

  11. M. Lazard, Bemerkungen zur Theorie der bewerteten Körper und Ringe,Math. Nach, 12 (1954), pp. 67–73.

    Article  MATH  MathSciNet  Google Scholar 

  12. E. Lutz, Sur l’équationy 2=x 3−Ax−B dans les corps p-adiques,J. Crelle, 177 (1937), pp. 238–247.

    MATH  Google Scholar 

  13. A. Mattuck, Abelian varieties overp-adic fields,Ann. Math., 62 (1955), pp. 92–119.

    Article  MathSciNet  Google Scholar 

  14. A. Néron, Valeur asymptotique du nombre des points de hauteur bornée sur une courbe elliptique,International Congress of Math., Edinburgh, 1958.

  15. M. Rosenlicht, Some basic theorems on algebraic groups,Amer. J. Math., 78, 1956, pp. 401–443.

    Article  MATH  MathSciNet  Google Scholar 

  16. P. Samuel, Algèbre locale,Mém. Sci. Math., no 123, Paris, Gauthier-Villars, 1953.

    Google Scholar 

  17. G. Shimura (cité [R]), Reduction of algebraic varieties with respect to a discrete valuation of the basic field,Amer. J. Math., 77 (1955), pp. 134–176.

    Article  MATH  MathSciNet  Google Scholar 

  18. J.-P. Serre,Groupes algébriques et corps de classes, Act. sc. et indust., no 1264, Paris, Hermann, 1959.

    MATH  Google Scholar 

  19. J.-P. Serre, Groupes proalgébriques,Publ. Math. Inst. Htes Ét. scientifiques, Paris, 7, 1962.

  20. J.-P. Serre,Corps locaux, Act. sc. et indust., no 1296, Paris, Hermann, 1962.

    MATH  Google Scholar 

  21. A. Weil (cité [F]).Foundations of Algebraic Geometry, Amer. Math. Soc. Colloquium Publ, vol. 29, New York, 1946, 2e éd.

    MATH  Google Scholar 

  22. A. Weil,Variétés abéliennes et courbes algébriques, Act. sc. et indust., no 1064, Paris, Hermann, 1948.

    MATH  Google Scholar 

  23. A. Weil, Arithmetic on algebraic varieties,Ann. Math. (2), 53 (1951), pp. 412–444.

    Article  MathSciNet  Google Scholar 

  24. A. Weil, The field of definition of a variety,Amer. J. Math., 78, no 3 (1956), pp. 509–524.

    Article  MATH  MathSciNet  Google Scholar 

  25. E. Witt, Zyklische Körper und Algebren der Charakteristikp vom Gradep n,J. Crelle, 176 (1936), pp. 126–140.

    MATH  Google Scholar 

  26. O. Zariski, The problem of minimal models in the theory of algebraic surfaces,Amer. J. Math., 80, no 1, 1958), pp. 146–184.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors

About this article

Cite this article

Néron, A. Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Publications Mathématiques de L’Institut des Hautes Scientifiques 21, 5–125 (1964). https://doi.org/10.1007/BF02684271

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02684271

Navigation