Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing


Author: Paul Vojta
Journal: J. Amer. Math. Soc. 5 (1992), 763-804
MSC: Primary 11G30; Secondary 11J25, 14G40, 14H25
DOI: https://doi.org/10.1090/S0894-0347-1992-1151542-9
MathSciNet review: 1151542
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [B] E. Bombieri, The Mordell conjecture revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17 (1990), 615-640. MR 1093712 (92a:11072)
  • [B-V] E. Bombieri and J. Vaaler, On Siegel's lemma, Invent. Math. 73 (1983), 11-32; addendum, ibid. 75 (1984), 377. MR 707346 (85g:11049a)
  • [F 1] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366; corrigendum, ibid. 75 (1984), 381. MR 718935 (85g:11026a)
  • [F 2] -, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133 (1991), 549-576. MR 1109353 (93d:11066)
  • [L 1] S. Lang, Fundamentals of diophantine geometry, Springer-Verlag, New York, 1983. MR 715605 (85j:11005)
  • [L 2] -, Introduction to Arakelov theory, Springer-Verlag, New York, 1988. MR 969124 (89m:11059)
  • [M] D. Mumford, A remark on Mordell's conjecture, Amer. J. Math. 87 (1965), 1007-1016. MR 0186624 (32:4083)
  • [R] K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20; corrigendum, ibid. 2 (1955), 168. MR 0072182 (17:242d)
  • [Sil] J. H. Silverman, Rational points on symmetric products of a curve, preprint 1989. MR 1109348 (92m:11060)
  • [T] A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135 (1909), 284-305.
  • [V 1] P. Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, New York, 1987. MR 883451 (91k:11049)
  • [V 2] -, On algebraic points on curves, Compositio Math. 78 (1991), 29-36. MR 1096125 (93b:11080)
  • [V 3] -, Mordell's conjecture over function fields, Invent. Math. 98 (1989), 115-138. MR 1010158 (90k:11076)
  • [V 4] -, Siegel's theorem in the compact case, Ann. of Math. (2) 133 (1991), 509-548. MR 1109352 (93d:11065)
  • [V 5] -, Arithmetic discriminants and quadratic points on curves, Arithmetic Algebraic Geometry, Texel 1989 (G. van der Geer, F. Oort, and J. H. M. Steenbrink, eds.), Prog. in Math., vol. 89, Birkhäuser, Boston, 1991, pp. 359-376. MR 1085268 (92j:11059)
  • [V 6] -, Applications of arithmetic algebraic geometry to diophantine approximations, Proceedings of CIME Conference, Trento, 1991, Lecture Notes in Mathematics, Springer-Verlag, Heidelberg (to appear). MR 1338861 (96c:11067)
  • [W] E. Wirsing, On approximation of algebraic numbers by algebraic numbers of bounded degree, 1969 Number Theory Institute, Proc. Sympos. Pure Math., vol. 20, Amer. Math. Soc., Providence, R.I., 1971, pp. 213-247. MR 0319929 (47:8470)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 11G30, 11J25, 14G40, 14H25

Retrieve articles in all journals with MSC: 11G30, 11J25, 14G40, 14H25


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1992-1151542-9
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society