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The proof of the mordell conjecture

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References

  1. Arakelov, S. (1971) Families of curves with fixed degeneracies,Math. USSR Izvestija 5: 1277–1302.

    Article  Google Scholar 

  2. Baily, W. L. and Borel, A. (1966) Compactification of arithmetic quotients of bounded symmetric domains,Ann. of Math. 84: 442–528.

    Article  MATH  MathSciNet  Google Scholar 

  3. Deligne, P. and Mumford, D. (1969) The irreducibility of the space of curves of a given genus,Publ. Math. 36: 75–110.

    Article  MATH  MathSciNet  Google Scholar 

  4. Fairings, G. (to appear) Calculus on arithmetic surfaces, Ann. of Math.

  5. Fairings, G. (to appear) Arakelov’s theorem for abelian varieties,Inv. Math.

  6. Manin, Ju (1963)Dokl. Akad. Nauk SSSR152; (1963) English translation,Soviet Math. 4: 1505–1507.

    Google Scholar 

  7. Mordell, L. J. (1922) Proc. Cambridge Philos. Soc, 179-192.

  8. Moret-Bailly, L. (1983) Varietes abeliennes polarisees sur les corps de fonctions, C.R. Acad. Sc. Paris 296: 267–270.

    MATH  MathSciNet  Google Scholar 

  9. Namikawa, Y. (1980) Toroidal compactification of Siegel spaces, Springer Lecture Notes Vol. 812. New York: Springer-Verlag.

    Google Scholar 

  10. Parshin, A. N. (1968) Algebraic curves over function fields I,Math. USSR Izvestija 2: 1145–1170.

    Article  Google Scholar 

  11. Raynaud, M. (1974) Schemas en groupes de type (p, …, p),Bull. Soc. Math. France 102: 241–280.

    MATH  MathSciNet  Google Scholar 

  12. Grauert, H. (1965) Mordell’s Vermutung über rationale Punkte aut algebraischen Kurven und Funktionenkörper,Publ. Math. I.H.E.S., Vol. 25.

  13. Shafarevich, I. R. (1962) I.C.M.

  14. Szpiro, L. (1979) Sur le théorème de rigidité de Parshin et Arakelov,Astérisque 64: 169–202.

    MATH  MathSciNet  Google Scholar 

  15. Täte, J. (1967) p-divisible groups, in Proceedings of a Conference on local fields (Driebergen, 1966), 158–183. Berlin: Springer-Verlag.

    Chapter  Google Scholar 

  16. Täte, J. (1966) Endomorphisms of abelian varieties over finite fields,Inv. Math 2: 134–144.

    Article  Google Scholar 

  17. Weil, A. (1980) Collected Works, Vol. III, p. 454. Berlin: Springer-Verlag.

    Google Scholar 

  18. Zarhin, J. G. (1974) Isogenies of abelian varieties over fields of finite characteristics,Math. USSR Sbornik 24: 451–461.

    Article  Google Scholar 

  19. Zarhin, J. G. (1974) A remark on endomorphisms of abelian varieties over function fields of finite characteristics,Math. USSR Izvestija 8: 477–480.

    Article  MathSciNet  Google Scholar 

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  1. Department of Mathematics, University of Chicago, 60637, Chicago, IL

    Spencer Bloch

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  1. Spencer Bloch
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Bloch, S. The proof of the mordell conjecture. The Mathematical Intelligencer 6, 41–47 (1984). https://doi.org/10.1007/BF03024155

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