×

zbMATH — the first resource for mathematics

Integral points on curves. (English) Zbl 0112.13402

PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] E. Artin andG. Whaples, Axiomatic characterization of fields by the product formula,Bull. Am. Math. Soc., vol. 51, no 7 (1945), pp. 469–492. · Zbl 0060.08302 · doi:10.1090/S0002-9904-1945-08383-9
[2] C. Chabauty, Sur les équations diophantiennes liées aux unités d’un corps de nombres algébriques fini, thèse,Annali di Math., 17 (1938), pp. 127–168. · Zbl 0019.00303 · doi:10.1007/BF02410698
[3] ———-, Sur les points rationnels des variétés algébriques dont l’irrégularité est supérieure à la dimension,Comptes rendus Académie des Sciences, Paris, 212 (1941), pp. 1022–1024.
[4] S. Lang, Introduction to algebraic geometry,Interscience, New York, 1959. · Zbl 0095.15301
[5] ———-, Abelian varieties,Interscience, New York, 1959.
[6] ———-, Unramified class field theory over function fields in several variables,Annals of Math., vol. 64, no 2 (1956), pp. 285–325. · Zbl 0089.26201 · doi:10.2307/1969975
[7] S. Lang andA. Néron, Rational points of abelian varieties in function fields,Am. J. of Math., vol. 81, no 1 (1959), pp. 95–118. · Zbl 0099.16103 · doi:10.2307/2372851
[8] K. Mahler, Über die rationalen Punkte auf Kurven vom Geschlecht Eins,J. Reine angew. Math., Bd. 170 (1934), pp. 168–178. · JFM 60.0159.03 · doi:10.1515/crll.1934.170.168
[9] T. Matsusaka, On algebraic families of positive divisors...,J. Math. Soc. Japan, vol. 5, no 2 (1953), pp. 118–136. · Zbl 0051.37901 · doi:10.2969/jmsj/00520113
[10] L. J. Mordell, On the rational solutions of the indeterminate equation of the third and fourth degrees,Proc. of the Cambridge Philos. Soc., 21 (1922). · JFM 48.0140.03
[11] A. Néron, Problèmes arithmétiques et géométriques rattachés à la notion de rang d’une courbe algébrique dans un corps,Bull. Soc. Math. France, 80 (1952), pp. 101–166.
[12] D. Ridout, Thep-adic generalization of the Thue-Siegel-Roth theorem,Mathematika, 5 (1958), pp. 40–48. · Zbl 0085.03501 · doi:10.1112/S0025579300001339
[13] K. F. Roth, Rational approximations to algebraic numbers,Mathematika, 2 (1955), pp. 1–20. · Zbl 0064.28501 · doi:10.1112/S0025579300000644
[14] C. L. Siegel, Über einige Anwendungen Diophantischer Approximationen,Abh. Preussischen Akademie der Wissenschaften, Phys. Math. Klasse (1929), pp. 41–69.
[15] A. Weil, Arithmetic on algebraic varieties,Annals of Math., vol. 53, no 3 (1951), pp. 412–444. · Zbl 0043.27002 · doi:10.2307/1969564
[16] ———-, L’arithmétique sur les courbes algébriques,Acta Mathematica, 52 (1928), pp. 281–315. · JFM 55.0713.01 · doi:10.1007/BF02592688
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.