A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing
HTML articles powered by AMS MathViewer
- by Paul Vojta
- J. Amer. Math. Soc. 5 (1992), 763-804
- DOI: https://doi.org/10.1090/S0894-0347-1992-1151542-9
- PDF | Request permission
References
- Enrico Bombieri, The Mordell conjecture revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17 (1990), no. 4, 615–640. MR 1093712
- E. Bombieri and J. Vaaler, On Siegel’s lemma, Invent. Math. 73 (1983), no. 1, 11–32. MR 707346, DOI 10.1007/BF01393823
- G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), no. 3, 349–366 (German). MR 718935, DOI 10.1007/BF01388432
- Gerd Faltings, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133 (1991), no. 3, 549–576. MR 1109353, DOI 10.2307/2944319
- Serge Lang, Fundamentals of Diophantine geometry, Springer-Verlag, New York, 1983. MR 715605, DOI 10.1007/978-1-4757-1810-2
- Serge Lang, Introduction to Arakelov theory, Springer-Verlag, New York, 1988. MR 969124, DOI 10.1007/978-1-4612-1031-3
- David Mumford, A remark on Mordell’s conjecture, Amer. J. Math. 87 (1965), 1007–1016. MR 186624, DOI 10.2307/2373258
- K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1–20; corrigendum, 168. MR 72182, DOI 10.1112/S0025579300000644
- Joseph H. Silverman, Rational points on symmetric products of a curve, Amer. J. Math. 113 (1991), no. 3, 471–508. MR 1109348, DOI 10.2307/2374836 A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135 (1909), 284-305.
- Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451, DOI 10.1007/BFb0072989
- Paul Vojta, On algebraic points on curves, Compositio Math. 78 (1991), no. 1, 29–36. MR 1096125
- Paul Vojta, Mordell’s conjecture over function fields, Invent. Math. 98 (1989), no. 1, 115–138. MR 1010158, DOI 10.1007/BF01388847
- Paul Vojta, Siegel’s theorem in the compact case, Ann. of Math. (2) 133 (1991), no. 3, 509–548. MR 1109352, DOI 10.2307/2944318
- Paul Vojta, Arithmetic discriminants and quadratic points on curves, Arithmetic algebraic geometry (Texel, 1989) Progr. Math., vol. 89, Birkhäuser Boston, Boston, MA, 1991, pp. 359–376. MR 1085268, DOI 10.1007/978-1-4612-0457-2_{1}7
- Paul Vojta, Applications of arithmetic algebraic geometry to Diophantine approximations, Arithmetic algebraic geometry (Trento, 1991) Lecture Notes in Math., vol. 1553, Springer, Berlin, 1993, pp. 164–208. MR 1338861, DOI 10.1007/BFb0084730
- Eduard A. Wirsing, On approximations of algebraic numbers by algebraic numbers of bounded degree, 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969) Amer. Math. Soc., Providence, R.I., 1971, pp. 213–247. MR 0319929
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- 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