Claude Chabauty

Claude Chabauty (May 4, 1910, in Oran – June 2, 1990, in Dieulefit) was a French mathematician.

Career

He was admitted in 1929 to the École normale supérieure in Paris.[1] In 1938 he obtained his doctorate with a thesis on number theory and algebraic geometry. Subsequently he was a professor in Strasbourg.[2] From 1954 on, and for 22 years, he was the director of the department of pure mathematics at the University of Grenoble.[3]

Mathematical work

He worked on Diophantine approximation and geometry of numbers, where he used both classical and p-adic analytic methods.[3] He introduced the Chabauty topology to generalise Mahler's compactness theorem from Euclidean lattices to more general discrete subgroups.[4]

His 1938 doctoral thesis,[5] developing ideas of Skolem,[6] is important in algebraic geometry. According to André Weil:

In his beautiful thesis, Chabauty ..., following ideas of Skolem ..., has shown how the method of p-adic completion, with respect to a more or less arbitrary prime p, can yield deep results about varieties over an algebraic number-field; there, as already in Skolem's work, the problem concerns the intersection of an algebraic variety and of a multiplicative group; by p-adic completion, the latter becomes an algebroid variety defined by linear differential equations.[7]

Notes and References

  1. ^ "L'annuaire - a-Ulm". Association des anciens élèves, élèves et amis de l’École normale supérieure. Archived from the original on May 20, 2015. Retrieved April 14, 2019.
  2. ^ "Claude Chabauty". Number Theory Web. Retrieved April 14, 2019.
  3. ^ a b special issue of Annales de l'Institut Fourier (vol. XXIX, Fasc. 1), March 1979, for Chabauty's retirement
  4. ^ Chabauty, Claude (1950). "Limite d'ensembles et géométrie des nombres". Bulletin de la Société Mathématique de France. 78: 143–151. doi:10.24033/bsmf.1412. S2CID 125105731.
  5. ^ Chabauty, Claude (1938). "Sur les équations diophantiennes liées aux unités d'un corps de nombres algébriques fini" (PDF). Annali di Matematica Pura ed Applicata. 17 (1): 127–168. doi:10.1007/BF02410698. S2CID 123856131.
  6. ^ Skolem, Th. (1935). "Einige Sätze über 𝔭-adische Potenzreihen mit Anwendung auf gewisse exponentielle Gleichungen". Mathematische Annalen. 111 (1): 399–424. doi:10.1007/BF01472228. ISSN 0025-5831. S2CID 121512248.
  7. ^ Weil, André (1950). "Number-theory and algebraic geometry". Proc. Intern. Math. Congress, Cambridge, Mass. Vol. 2. pp. 90–100. (quote from p. 94)


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