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Finite descent obstruction for curves over function fields

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Abstract

We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of integral points on integral models of twists of modular curves over function fields.

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References

  1. J.D. Achter. Split reductions of simple abelian varieties. Math. Res. Lett., 16 (2009), 199–213.

    MathSciNet  MATH  Google Scholar 

  2. P. Deligne. Les constantes des equations fonctionnelles des fonctions L, in Modular Functions of One Variable II. Springer Lecture Notes in Mathematics, 349 (1973), 501–597.

    Article  MathSciNet  Google Scholar 

  3. J.-M. Fontaine and B. Mazur. Geometric Galois representations, in Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993), Int. Press, Cambridge, MA, (1995), pp. 41–78.

    Google Scholar 

  4. D. Harari and J.F. Voloch. The Brauer-Manin obstruction for integral points on curves. Math. Proc. Cam. Phil. Soc., 149 (2010), 413–421.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Helm and J.F. Voloch. Finite descent obstruction on curves and modularity. BLMS, to appear.

  6. B. Poonen and J.F. Voloch. The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Annals of Math., 171 (2010) 511–532.

    Article  MathSciNet  MATH  Google Scholar 

  7. V. Scharaschkin. Local-global problems and the Brauer-Maninobstruction, 1999, Ph.D. thesis, University of Michigan.

  8. A. Skorobogatov. Torsors and rational points. Cambridge University Press, Cambridge (2001).

    Book  MATH  Google Scholar 

  9. M. Stoll. Finite descent and rational points on curves. Algebra and Number Theory, 2(5) (2008), 595–611.

    Article  MathSciNet  Google Scholar 

  10. C.-L. Sun. Adelic points of subvarieties of isotrivial semi-abelian varieties over a global field of positive characteristic. arXiv:1005.4998.

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Correspondence to José Felipe Voloch.

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Voloch, J.F. Finite descent obstruction for curves over function fields. Bull Braz Math Soc, New Series 43, 1–6 (2012). https://doi.org/10.1007/s00574-012-0001-7

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  • DOI: https://doi.org/10.1007/s00574-012-0001-7

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