Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Siegel's theorem for complex function fields


Author: José Felipe Voloch
Journal: Proc. Amer. Math. Soc. 121 (1994), 1307-1308
MSC: Primary 11G05; Secondary 11G30, 14G25
DOI: https://doi.org/10.1090/S0002-9939-1994-1209430-9
MathSciNet review: 1209430
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a short proof of the finiteness of the set of integral points on an affine algebraic curve of genus at least one, defined over a function field of characteristic zero.


References [Enhancements On Off] (What's this?)

  • [BV] A. Buium and J. F. Voloch, Integral points of abelian varieties over function fields of characteristic zero, Math. Ann. 297 (1993), 303-307. MR 1241808 (94i:14029)
  • [F] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpen, Invent. Math. 73 (1983), 349-366. MR 718935 (85g:11026a)
  • [L] S. Lang, Integral points on curves, Inst. Hautes Études Sci. Publ. Math. 6 (1960), 27-43. MR 0130219 (24:A86)
  • [M] Yu. I. Manin, Rational points on an algebraic curve over function fields, Izv. Acad. Nauk USSR (1963) and Letter to the editor, Math. USSR-Izv. 34 (1990), 465-466; English transl., Transl. Amer. Math. Soc. Ser. 2, vol. 50, Amer. Math. Soc., Providence, RI, 1966, pp. 189-234. MR 998307 (90f:11039)
  • [Ms] R. C. Mason, Diophantine equations over function fields, London Math. Soc. Lecture Note Ser., vol. 96, Cambridge Univ. Press, Cambridge, 1984. MR 754559 (86b:11026)
  • [S] J. H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Math., vol. 106, Springer, New York, 1986. MR 817210 (87g:11070)
  • [Si] C. L. Siegel, Einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys. Math. Kl. 1 (1929), 41-69.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11G05, 11G30, 14G25

Retrieve articles in all journals with MSC: 11G05, 11G30, 14G25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1209430-9
Keywords: Algebraic curves, function fields, integral points
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society