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ON CONTRACTION OF ALGEBRAIC POINTS

  • Bogomolov, Fedor (Courant Institute of Mathematical Sciences New York University) ;
  • Qian, Jin (Courant Institute of Mathematical Sciences New York University)
  • Received : 2016.08.17
  • Accepted : 2017.03.07
  • Published : 2017.09.30

Abstract

We study contraction of points on ${\mathbb{P}}^1({\bar{\mathbb{Q}}})$ with certain control on local ramification indices, with application to the unramified curve correspondence problem initiated by Bogomolov and Tschinkel.

Acknowledgement

Supported by : New York University

References

  1. G. V. Belyi, Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 2, 267-276.
  2. G. V. Belyi, Another proof of three points theorem, Max Planck Institute Preprint, MPI, 1997.
  3. F. Bogomolov and Y. Tschinkel, Unramified Correspondences, Algebraic Number Theory and Algebraic Geometry, 17-25, Contemp. Math., vol. 300, Amer. Math. Soc., Providence, RI, 2002.
  4. F. Bogomolov and Y. Tschinkel, Couniformization of curves over number fields, Geometric Methods in Algebra and Number Theory, 43-57, Progress in Mathematics, vol. 235, Birkhauser, 2005.
  5. F. Bogomolov and Y. Tschinkel, Curves in abelian varieties over finite fields, Int. Math. Res. Not. 2005 (2005), no. 4, 233-238. https://doi.org/10.1155/IMRN.2005.233
  6. E. Bombieri and W. Gubler, Heights in Diophantine Geometry, Cambridge University Press, 2006.
  7. H. Stichtenoth, Algebraic function fields and codes, Graduate Texts in Mathematics, Vol. 254, 2ed, Springer-Verlag, New York, 2009.