Beppo Levi and the arithmetic of elliptic curves.

Norbert Schappacher (1)

1 IRMA - Institut de Recherche Mathématique Avancée

"In this article we describe Beppo Levi's (1875--1961) life and mathematical work, with special emphasis on his forgotten contributions to the arithmetic of elliptic curves. Most students of mathematics encounter the name of the Italian mathematician Beppo Levi in integration theory, when they learn ``Beppo Levi's Lemma"" on integrals of monotone sequences of functions. The attribution of this result is historically correct, but it by no means exhausts Beppo Levi's mathematical accomplishments. In fact, in his address to the 1908 {\sl International Congress of Mathematicians\/} in Rome, Beppo Levi anticipated explicitly, by more than 60 years, a famous conjecture about torsion points on elliptic curves over $\QQ$ which was made again by Andrew P.~Ogg in 1970, and proved by Barry Mazur in~1976. The last twenty years of Beppo Levi's long life were devoted to building up mathematics in Rosario, Argentina, the place where he had emigrated."

Mots clés: "Biography; arithmetic of elliptic curves over $\QQ$; integration; singularities of algebraic surfaces"; Biography; singularities of algebraic surfaces

Domaines: Histoire et perspectives sur les mathématiques [math.HO]

Norbert Schappacher. Beppo Levi and the arithmetic of elliptic curves.. 1995. ⟨hal-00129719⟩