André Néron

André Néron (French pronunciation: [ɑ̃dʁe neʁɔ̃]; November 30, 1922, La Clayette, France – April 6, 1985, Paris, France) was a French mathematician at the Université de Poitiers who worked on elliptic curves and abelian varieties. He discovered the Néron minimal model of an elliptic curve or abelian variety, the Néron differential, the Néron–Severi group, the Néron–Ogg–Shafarevich criterion, the local height and Néron–Tate height of rational points on an abelian variety over a discrete valuation ring or Dedekind domain, and classified the possible fibers of an elliptic fibration.

André Néron
Born	(1922-11-30)30 November 1922 La Clayette, France
Died	6 April 1985(1985-04-06) (aged 62) Paris, France
Known for	Néron differential Néron model Néron–Severi group Néron–Tate height Néron–Ogg–Shafarevich criterion
Awards	Émile Picard Medal (1983) ICM Speaker (1954)
Scientific career
Fields	Mathematics
Institutions	Université de Poitiers
Doctoral advisor	Albert Châtelet
Doctoral students	Jean-Louis Colliot-Thélène

Life and career

He was a student of Albert Châtelet, and his PhD students were Jean-Louis Colliot-Thélène, Gérard Ligozat, and Dimitrios Poulakis.

He gave invited talks at the International Congress of Mathematicians in 1954 and 1966 (Néron 1956, 1968). In 1983 the Académie des sciences awarded him the Émile Picard Medal.

He died of cancer in 1985.

Publications

• Néron, André (1952), "Problèmes arithmétiques et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps", Bulletin de la Société Mathématique de France, 80: 101–166, doi:10.24033/bsmf.1427, ISSN 0037-9484, MR 0056951
• Néron, André (1956), "Propriétés arithmétiques de certaines familles de courbes algébriques", Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, Erven P. Noordhoff N.V., Groningen, pp. 481–488, MR 0087210, archived from the original on 2016-09-17, retrieved 2011-12-14
• Néron, André (1964), "Modèles minimaux des variétés abéliennes sur les corps locaux et globaux", Publications Mathématiques de l'IHÉS, 21: 5–128, doi:10.1007/BF02684271, ISSN 1618-1913, MR 0179172, S2CID 120802890
• Néron, André (1968), "Degré d'intersection en géométrie diophantienne", Proceedings of International Congress of Mathematicians (Moscow, 1966), Izdat. Mir, Moscow, pp. 485–495, MR 0240097, archived from the original on 2012-03-16, retrieved 2011-12-14

References

• Bosch, Siegfried; Lütkebohmert, Werner; Raynaud, Michel (1990), Néron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 21, Berlin, New York: Springer-Verlag, ISBN 978-3-540-50587-7, MR 1045822
• Association amicale des anciens élèves de l'École normale supérieure, l'École normale supérieure, 1986, p. 117

External links

• Neron on mathoverflow