Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Siegel’s theorem for complex function fields
HTML articles powered by AMS MathViewer

by José Felipe Voloch PDF
Proc. Amer. Math. Soc. 121 (1994), 1307-1308 Request permission

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
  • Alexandru Buium and José Felipe Voloch, Integral points of abelian varieties over function fields of characteristic zero, Math. Ann. 297 (1993), no. 2, 303–307. MR 1241808, DOI 10.1007/BF01459503
  • G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), no. 3, 349–366 (German). MR 718935, DOI 10.1007/BF01388432
  • Serge Lang, Integral points on curves, Inst. Hautes Études Sci. Publ. Math. 6 (1960), 27–43. MR 130219, DOI 10.1007/BF02698777
  • Yu. I. Manin, Letter to the editors: “Rational points on algebraic curves over function fields” [Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 1397–1442; MR0157971 (28 #1199)], Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 2, 447–448 (Russian); English transl., Math. USSR-Izv. 34 (1990), no. 2, 465–466. MR 998307
  • R. C. Mason, Diophantine equations over function fields, London Mathematical Society Lecture Note Series, vol. 96, Cambridge University Press, Cambridge, 1984. MR 754559, DOI 10.1017/CBO9780511752490
  • Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210, DOI 10.1007/978-1-4757-1920-8
  • 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
  • © Copyright 1994 American Mathematical Society
  • 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