Pierre Émile Cartier (born 10 June 1932) is 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 O ...

. An associate of the

Bourbaki group Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in ...

and at one time a colleague of Alexander Grothendieck, his interests have ranged over

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrica ...

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

, and

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

. He studied at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savo ...

Paris Paris () is the capital and 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), making it the 30th most densely populated city in the world in 2020. S ...

under

Henri Cartan Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of co ...

and

André Weil André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. Th ...

. Since his 1958

thesis A thesis ( : theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: ...

on algebraic geometry he has worked in a number of fields. He is known for the introduction of the

Cartier operator Cartier may refer to: People * Cartier (surname), a surname (including a list of people with the name) * Cartier Martin (born 1984), American basketball player Places * Cartier Island, an island north-west of Australia that is part of Australi ...

in algebraic geometry in characteristic ''p'', and for work on duality of

abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functio ...

and on

formal group In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one o ...

s. He is the eponym of

Cartier divisor In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil by David Mumfo ...

s and

Cartier duality In mathematics, Cartier duality is an analogue of Pontryagin duality for commutative group schemes. It was introduced by . Definition using characters Given any finite flat commutative group scheme ''G'' over ''S'', its Cartier dual is the group o ...

. From 1961 to 1971 he was a professor at the

University of Strasbourg The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers. The French university traces its history to the ...

. In 1970 he was an Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renam ...

in Nice. He was awarded the 1978

Prize Ampère A prize is an award to be given to a person or a group of people (such as sporting teams and organizations) to recognize and reward their actions and achievements.

of the

French Academy of 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 the ...

. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Publications

* (1st edition 1969) * (1st edition 1992) * * ''Freedom in Mathematics'', Springer India, 2016 (with Cédric Villani, Jean Dhombres, Gerhard Heinzmann), . ** Translation from the French language edition: ''Mathématiques en liberté'', La Ville Brûle, Montreuil 2012, . * Pierre Cartier: ''Alexander Grothendieck. A country known only by name.'' Notices AMS, vol. 62, 2015, no. 4, pp. 373–382
PDF.
h2>

as editor

* (1st edition 1990) *

References

External links

Cartier's website
at the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, jus ...

, with a photograph, CV, and list of publications
Issue of Moscow Mathematical Journal dedicated to Pierre Cartier
*
Javier Fresán ''The Castle of Groups'', Interview with Pierre Cartier, EMS Newsletter 2009, pdf
* * * * 1932 births Living people People from Sedan, Ardennes École Normale Supérieure alumni University of Strasbourg faculty 20th-century French mathematicians 21st-century French mathematicians Institute for Advanced Study visiting scholars Nicolas Bourbaki Fellows of the American Mathematical Society {{France-mathematician-stub