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Deformation of integral sections in the Mordell–Weil group

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Abstract

Using deformation theory, we answer two questions of Shioda concerning the infinitesimal structure of the moduli space of integral sections in the Mordell–Weil group.

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References

  1. Badescu, L.: Algebraic Surfaces. Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author. Universitext. Springer, New York (2001)

  2. Hartshorne, R.: Deformation Theory. Springer, New York (2010)

    Book  MATH  Google Scholar 

  3. Liu, Q.: Algebraic Geometry and Arithmetic Curves. Oxford Graduate Texts in Mathematics, vol. 6. Oxford Univ. Press, Oxford (2002)

    Google Scholar 

  4. Schütt, M., Shioda, T.: Mordell-Weil Lattices. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 70. Springer, Singapore (2019)

  5. Shioda, T.: On the Mordell-Weil lattices. Comment. Math. Univ. St. Paul 39(2), 211–240 (1990)

    MathSciNet  MATH  Google Scholar 

  6. Shioda, T.: Integral points and Mordell-Weil lattices. In: G. Wüstholz (Ed.) A Panorama of Number Theory or the View from Baker’s Garden (Zurich 1999), pp. 185–193. Cambridge University Press, Cambridge (2002)

  7. Shioda, T.: Grobner Basis, Mordell-Weil lattices and deformation of singularities, I. Proc. Japan Acad. Ser. A Math. Sci. 86(2), 21–26 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Shioda, T.: Grobner Basis, Mordell-Weil lattices and deformation of singularities, II. Proc. Japan Acad. Ser. A Math. Sci. 86(2), 27–32 (2010)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Yi Gu.

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Gong, C., Gu, Y. Deformation of integral sections in the Mordell–Weil group. Arch. Math. 120, 373–379 (2023). https://doi.org/10.1007/s00013-023-01828-3

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  • DOI: https://doi.org/10.1007/s00013-023-01828-3

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