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A higher dimensional analogue of Mordell's conjecture over function fields

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References

  1. Grauert, H.: Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper. Publ. Math. I.H.E.S.25 131–149 (1965)

    Google Scholar 

  2. Grothendieck, A., Dieudonné, J.: Élements de géometrie algébrique. II. Publ. Math. I.H.E.S.8 (1961)

  3. Grothendieck, A., Dieudonné, J.: Éléments de géometrie algébrique. III. Publ. Math. I.H.E.S.17 (1963)

  4. Hartshorne, R.: Algebraic geometry. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  5. Hartshorne, R.: Ample vector bundles. Publ. Math. I.H.E.S.29, 63–94 (1966)

    Google Scholar 

  6. Kalka, M.: Deformation of submanifolds of strongly negatively curved manifolds. Math. Ann.251, 243–248 (1980)

    Google Scholar 

  7. Kalka, M., Shiffman, B., Wong., B.: Finiteness and rigidity theorems for holomorphic mappings (to appear in Michigan Math. J.)

  8. Kobayashi, S.: Negative vector bundles and complex Finsler structures. Nagoya Math. J57, 153–166 (1975)

    Google Scholar 

  9. Lang, S.: Higher dimensional Diophantine problems. Bull. Am. Math. Soc.80, 779–787 (1974)

    Google Scholar 

  10. Manin, Ju.: A proof of the analogue of the Mordell conjecture for algebraic curves over function fields. Dokl. Akad. Nauk. SSSR152, 1061–1063 (1963)

    Google Scholar 

  11. Manin, Ju.: Rational points of algebraic curves over function fields. Izv. Akad. Nauk. SSSR, Ser. Mat.27, 1395–1440 (1963)

    Google Scholar 

  12. Miwa, M.: On Mordell's conjecture for algebraic curves over function fields. J. Math. Soc. Japan18, 182–188 (1966)

    Google Scholar 

  13. Noguchi, J., Sunada, T.: Finiteness of the family of rational and meromorphic mappings into algebraic varieties (to appear in Am. J. Math.)

  14. Samuel, P.: Compléments à un article de Hans Grauert sur la conjecture de Mordell. Publ. Math. I.H.E.S.29, 55–62 (1966)

    Google Scholar 

  15. Samuel, P.: Lectures on old and new results on algebraic curves. Tata Institute of Fundamental Research, Bombay, 1966

    Google Scholar 

  16. Sunada, T.: Holomorphic mappings into a compact quotient of symmetric bounded domain. Nagoya Math. J.64, 159–175 (1976)

    Google Scholar 

  17. Urata, T.: Holomorphic mappings into a certain compact complex analytic space (preprint)

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Supported in part by NSF grant MCS 77-18723 A04 and by the Sakkokai, Foundation

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Noguchi, J. A higher dimensional analogue of Mordell's conjecture over function fields. Math. Ann. 258, 207–212 (1981). https://doi.org/10.1007/BF01450536

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