[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160680

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1577-1596 More about this Journal

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.

Keywords

unramified correspondences; Abyhankar's lemma; contraction of points;

Citations & Related Records

Reference

1	H. Stichtenoth, Algebraic function fields and codes, Graduate Texts in Mathematics, Vol. 254, 2ed, Springer-Verlag, New York, 2009.
2	G. V. Belyi, Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 2, 267-276.
3	G. V. Belyi, Another proof of three points theorem, Max Planck Institute Preprint, MPI, 1997.
4	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.
5	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.
6	F. Bogomolov and Y. Tschinkel, Curves in abelian varieties over finite fields, Int. Math. Res. Not. 2005 (2005), no. 4, 233-238. DOI
7	E. Bombieri and W. Gubler, Heights in Diophantine Geometry, Cambridge University Press, 2006.