André Néron (November 30, 1922,

La Clayette La Clayette () is a commune in the east-central French department of Saône-et-Loire. Geography La Clayette is situated in the southernmost part of Burgundy, north of the historical province of Beaujolais. It belongs to an area designated sinc ...

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area ...

– April 6, 1985,

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

, France) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

at the

Université de Poitiers The University of Poitiers (UP; french: Université de Poitiers) is a public university located in Poitiers, France. It is a member of the Coimbra Group. It is multidisciplinary and contributes to making Poitiers the city with the highest stud ...

who worked on

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s and

abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a Algebraic variety#Projective variety, projective algebraic variety that is also an algebraic group, i.e., has a group law th ...

. He discovered the

Néron minimal model Neron or Néron may refer to: *Neron (DC Comics), a fictional character in the DC Comics' universe. * An alternative name of the Roman Emperor Nero * André Néron, a mathematician, who introduced: ** Néron minimal model ** Néron differential ...

of an elliptic curve or abelian variety, the

Néron differential In mathematics, a Néron differential, named after André Néron, is an almost canonical choice of 1-form on an elliptic curve or abelian variety defined over a local field or global field. The Néron differential behaves well on the Néron minimal ...

, the

Néron–Severi group In algebraic geometry, the Néron–Severi group of a variety is the group of divisors modulo algebraic equivalence; in other words it is the group of components of the Picard scheme of a variety. Its rank is called the Picard number. It is nam ...

, the

Néron–Ogg–Shafarevich criterion In mathematics, the Néron–Ogg–Shafarevich criterion states that if ''A'' is an elliptic curve or abelian variety over a local field ''K'' and ℓ is a prime not dividing the characteristic of the residue field of ''K'' then ''A'' has good re ...

, the local height and

Néron–Tate height In number theory, the Néron–Tate height (or canonical height) is a quadratic form on the Mordell–Weil group of rational points of an abelian variety defined over a global field. It is named after André Néron and John Tate. Definition and p ...

rational point In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers is generally understood. If the field is the fiel ...

s on an abelian variety over a

discrete valuation ring In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an integral domain ''R'' which satisfies any one of the following equivalent conditions: # ''R'' i ...

Dedekind domain In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily ...

, and classified the possible fibers of an elliptic fibration.

Life and career

He was a student of

Albert Châtelet Albert Châtelet (24 October 1883 – 30 June 1960) was a French politician and mathematician. Biography Châtelet was a student at the École normale supérieure (Paris) from 1905 to 1908, succeeding to the Agrégation (a highly selective compe ...

, and his PhD students were Jean-Louis Colliot-Thélène and Gérard Ligozat. He gave invited talks at the International Congress of Mathematicians in 1954 and 1966 . In 1983 the

Académie des sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...

awarded him the

Émile Picard Medal The Émile Picard Medal (or Médaille Émile Picard) is a medal named for Émile Picard awarded every 6 years to an outstanding mathematician by the Institut de France, Académie des sciences. This rewards a mathematician designated by the Academy ...

. He died of cancer in 1985.

Publications

* * * *

References

* *

External links

Neron on mathoverflow
1922 births 1985 deaths École Normale Supérieure alumni Academic staff of the University of Poitiers 20th-century French mathematicians Algebraic geometers Number theorists Deaths from cancer in France People from Saône-et-Loire {{france-mathematician-stub