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Mordell's finite basis theorem revisited

  • J. W. S. Cassels (a1)

0. Mordell proved his ‘Finite Basis Theorem’ in the paper [31] ‘On the rational solutions of the indeterminate equations of the third and fourth degrees’ which appeared in 1922 in Volume 21 of these Proceedings. It had been assumed, rather than conjectured, by Poincaré some 20 years previously, but it was not what he had set out to prove. The theorem and its generalizations are at the heart of many of the most interesting achievements and problems of the theory of numbers and also of algebraic geometry. Mordell himself had virtually no part in these developments: his great work was to lie elsewhere ([5]).

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[5]J. W. S. Cassels . L. J. Mordell . Biog. Mem. Roy. Soc. 19 (1973), 493520.

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[36]M. Noether . Über Flächen, weiche Schaaren rationaler Curven besitzen. Math. Ann. 3 (1871), 161227.

[40]P. Samuel . Compléments à un article de Hans Grauert sur la conjecture de Mordell. Inst. Hautes Études Sci. Publ. Math. 29 (1966), 5562.

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[47]J. Tate . The arithmetic of elliptic curves. Invent. Math. 23 (1974), 179206.

[52]A. Weil . L'arithmétique sur les courbes algébriques. Acta Math. 52 (1928), 281315 (= Coll. Papers I, 11–45).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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