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Complements to Mordell

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Part of the book series: Aspects of Mathematics ((ASMA,volume 6))

Abstract

The purpose of this chapter is to give some additional results, mainly about generalizations to finitely generated extensions of Q. Similar results have been obtained by other people, and on occasion I have used their arguments instead of my original ones. More precisely, we obtain the following facts:

Choose a finitely generated extension field K of Q and let R K denote a finitely generated smooth Z-algebra, with field of quotients K. As before, π=Gal(K̄/K) is the absolute Galois-group of K.

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Bibliography

  1. S. Lang: Division points on curves Annalli di Matematicce Pura ed Applicata, ser. 4, 70 (1965), 229–234.

    MATH  Google Scholar 

  2. J.C. Lagarias/ A.M. Odlyzko: Effective versions of the Chebotarev density theorem Proc. Sympos. Univ. Durham 1975, 409–464. Academic Press, London 1977.

    Google Scholar 

  3. D. Mumford: A remark on Mordell’s conjecture Amer. J. Math. 87 (1965), 1007–1016.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Raynaud: Courbes sur une varieté abélienne et points de torsion. Invent. Math. 71 (1983), 207–233.

    Article  MathSciNet  MATH  Google Scholar 

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© 1986 Springer Fachmedien Wiesbaden

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Faltings, G. (1986). Complements to Mordell. In: Rational Points. Aspects of Mathematics, vol 6. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06812-9_6

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  • DOI: https://doi.org/10.1007/978-3-663-06812-9_6

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-18593-0

  • Online ISBN: 978-3-663-06812-9

  • eBook Packages: Springer Book Archive

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