Claude Chabauty

Claude Chabauty (born May 4, 1910 in Oran, died 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, Chaubaty ..., 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. 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.
  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.
  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.
  7. Weil, André (1950). "Number-theory and algebraic geometry". Proc. Intern. Math. Congress, Cambridge, Mass. 2. pp. 90–100. (quote from p. 94)


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