Jean-Pierre Serre (; born 15 September 1926) 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
On ...
who has made contributions to
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
,
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 geometrical ...
, and
algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
. He was awarded the
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
in 1954, the
Wolf Prize
The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...
in 2000 and the inaugural
Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. ...
in 2003.
Biography
Personal life
Born in
Bages,
Pyrénées-Orientales
Pyrénées-Orientales (; ca, Pirineus Orientals ; oc, Pirenèus Orientals ; ), also known as Northern Catalonia, is a department of the region of Occitania, Southern France, adjacent to the northern Spanish frontier and the Mediterranean Sea. ...
,
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
, to pharmacist parents, Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 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, Savoi ...
in
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 ...
. He was awarded his doctorate from the
Sorbonne in 1951. From 1948 to 1954 he held positions at the
Centre National de la Recherche Scientifique in
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 ...
. In 1956 he was elected professor at the
Collège de France, a position he held until his retirement in 1994. His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer
Claudine Monteil. The French mathematician
Denis Serre
Denis Serre (born 1 November 1954) is a French mathematician who works as a professor at the École normale supérieure de Lyon, where he has chaired the mathematics department since 2012. is his nephew. He practices skiing, table tennis, and rock climbing (in
Fontainebleau
Fontainebleau (; ) is a commune in the metropolitan area of Paris, France. It is located south-southeast of the centre of Paris. Fontainebleau is a sub-prefecture of the Seine-et-Marne department, and it is the seat of the ''arrondissement ...
).
Career
From a very young age he was an outstanding figure in the school of
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 ...
, working on
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
,
several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variable ...
and then
commutative algebra
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...
and
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 geometrical ...
, where he introduced
sheaf theory and
homological algebra
Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precurs ...
techniques. Serre's thesis concerned the
Leray–Serre spectral sequence associated to a
fibration
The notion of a fibration generalizes the notion of a fiber bundle and plays an important role in algebraic topology, a branch of mathematics.
Fibrations are used, for example, in postnikov-systems or obstruction theory.
In this article, all map ...
. Together with Cartan, Serre established the technique of using
Eilenberg–MacLane spaces for computing
homotopy groups of spheres, which at that time was one of the major problems in topology.
In his speech at the Fields Medal award ceremony in 1954,
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...
gave high praise to Serre, and also made the point that the award was for the first time awarded to a non-analyst. Serre subsequently changed his research focus.
Algebraic geometry
In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger
Alexander Grothendieck led to important foundational work, much of it motivated by the
Weil conjectures. Two major foundational papers by Serre were ''Faisceaux Algébriques Cohérents'' (FAC, 1955), on
coherent cohomology In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties. Many geometric questions can be formulated as questions about the exist ...
, and ''Géométrie Algébrique et Géométrie Analytique'' (
GAGA, 1956).
Even at an early stage in his work Serre had perceived a need to construct more general and refined
cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...
theories to tackle the Weil conjectures. The problem was that the cohomology of a
coherent sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with refe ...
over a
finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...
could not capture as much topology as
singular cohomology with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based on
Witt vector coefficients.
Around 1958 Serre suggested that isotrivial principal bundles on algebraic varieties – those that become trivial after pullback by a finite
étale map In mathematics, more specifically in algebra, the adjective étale refers to several closely related concepts:
* Étale morphism
** Formally étale morphism
* Étale cohomology
* Étale topology
* Étale fundamental group
* Étale group scheme
* ...
– are important. This acted as one important source of inspiration for Grothendieck to develop the
étale topology In algebraic geometry, the étale topology is a Grothendieck topology on the category of schemes which has properties similar to the Euclidean topology, but unlike the Euclidean topology, it is also defined in positive characteristic. The étale ...
and the corresponding theory of
étale cohomology. These tools, developed in full by Grothendieck and collaborators in
Séminaire de géométrie algébrique (SGA) 4 and SGA 5, provided the tools for the eventual proof of the Weil conjectures by
Pierre Deligne.
Other work

From 1959 onward Serre's interests turned towards
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
,
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...
, in particular
Galois representations
In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring i ...
and
modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...
s.
Amongst his most original contributions were: his "
Conjecture II" (still open) on Galois cohomology; his use of
group actions
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...
on
trees (with
Hyman Bass); the Borel–Serre compactification; results on the number of points of curves over finite fields;
Galois representation
In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring i ...
s in
ℓ-adic cohomology and the proof that these representations have often a "large" image; the concept of ''p''-adic
modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...
; and the
Serre conjecture (now a theorem) on mod-''p'' representations that made
Fermat's Last Theorem a connected part of mainstream
arithmetic geometry.
In his paper FAC, Serre asked whether a finitely generated
projective module
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizati ...
over a
polynomial ring
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) ...
is
free
Free may refer to:
Concept
* Freedom, having the ability to do something, without having to obey anyone/anything
* Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism
* Emancipate, to procur ...
. This question led to a great deal of activity in
commutative algebra
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...
, and was finally answered in the affirmative by
Daniel Quillen and
Andrei Suslin
Andrei Suslin (russian: Андре́й Алекса́ндрович Су́слин, sometimes transliterated Souslin) was a Russian mathematician who contributed to algebraic K-theory and its connections with algebraic geometry. He was a Trustee ...
independently in 1976. This result is now known as the
Quillen–Suslin theorem
The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between free modules and projective modules over polynomial rings. In the geometric setting it is ...
.
Honors and awards
Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded the
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
. He went on to win the
Balzan Prize
The International Balzan Prize Foundation awards four annual monetary prizes to people or organizations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the br ...
in 1985, the
Steele Prize
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have ...
in 1995, the
Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...
in 2000, and was the first recipient of the
Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. ...
in 2003. He has been awarded other prizes, such as the Gold Medal of the French National Scientific Research Centre (Centre National de la Recherche Scientifique, CNRS).
He is a foreign member of several scientific Academies (France, US, Norway, Sweden, Russia, the Royal Society,
Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...
(1978),
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
,
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
, the
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...
) and has received many honorary degrees (from Cambridge, Oxford, Harvard, Oslo and others). 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, ...
.
Serre has been awarded the highest honors in France as
Grand Cross of the Legion of Honour
The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon B ...
(Grand Croix de la Légion d'Honneur) and
Grand Cross of the Legion of Merit (Grand Croix de l'Ordre National du Mérite).
See also
*
List of things named after Jean-Pierre Serre
These are the things named after Jean-Pierre Serre, a French mathematician.
*Bass–Serre theory
*Serre class
*Quillen–Suslin theorem (sometimes known as "Serre's Conjecture" or "Serre's problem")
*Serre conjecture (number theory), Serre's Conjec ...
*
Multiplicity (mathematics)
*
Nicolas Bourbaki
Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally in ...
*
p-adic modular form
In mathematics, a ''p''-adic modular form is a ''p''-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. introduced ''p''-adic modular forms as limits of ordinary modular forms, and shortly afterw ...
Bibliography
*''Groupes Algébriques et Corps de Classes'' (1959), Hermann , translated into English as
**
*''Corps Locaux'' (1962), Hermann , as
**
*''Cohomologie Galoisienne'' (1964) Collège de France course 1962–63, as
**
*''Algèbre Locale, Multiplicités'' (1965) Collège de France course 1957–58, as
**
*
*''Algèbres de Lie Semi-simples Complexes'' (1966), as
**
*''Abelian ℓ-Adic Representations and Elliptic Curves'' (1968), reissue,
*''Cours d'arithmétique'' (1970), PUF, as
**
*''Représentations linéaires des groupes finis'' (1971), Hermann, as
**
*''Arbres, amalgames, SL
2'' (1977), SMF, as
**
*''Oeuvres/Collected Papers in four volumes'' (1986) Vol. IV in 2000, Springer-Verlag
**
**
**
**
*
*
* ''Exposés de séminaires 1950–1999 '' (2001), SMF, ,
*
*
*
* ''Correspondance Serre-Tate '' (2015), edited with
Pierre Colmez
Pierre Colmez (born 1962) is a French mathematician, notable for his work on ''p''-adic analysis.
Colmez studied at École Normale Supérieure and obtained his doctorate from Grenoble University. He won the 2005 Fermat Prize for his contribution ...
, SMF,
* ''Finite Groups: an Introduction'' (2016), Higher Education Press & International Press,
* ''Rational Points on Curves over Finite Fields'' (2020), with contributions by
E. Howe
E is the fifth letter of the Latin alphabet.
E or e may also refer to:
Commerce and transportation
* €, the symbol for the euro, the European Union's standard currency unit
* ℮, the estimated sign, an EU symbol indicating that the weigh ...
,
J. Oesterlé
''J. The Jewish News of Northern California'', formerly known as ''Jweekly'', is a weekly print newspaper in Northern California, with its online edition updated daily. It is owned and operated by San Francisco Jewish Community Publications In ...
,
C. Ritzenthaler, SMF,
A list of corrections, and updating, of these books can be found on his home page at Collège de France.
Notes
External links
*
*
Jean-Pierre Serre, Collège de France, biography and publications.at the
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
, in French.
Interview with Jean-Pierre Serrein Notices of the American Mathematical Society.
An Interview with Jean-Pierre Serreby C.T. Chong and Y.K. Leong, National University of Singapore.
How to write mathematics badlya public lecture by Jean-Pierre Serre on writing mathematics.
(in French)
{{DEFAULTSORT:Serre, Jean-Pierre
1926 births
Living people
People from Pyrénées-Orientales
Foreign associates of the National Academy of Sciences
20th-century French mathematicians
Abel Prize laureates
Algebraic geometers
Algebraists
École Normale Supérieure alumni
École Normale Supérieure faculty
Nicolas Bourbaki
Fields Medalists
Collège de France faculty
Foreign Members of the Royal Society
Number theorists
Topologists
University of Paris alumni
Grand Croix of the Légion d'honneur
Wolf Prize in Mathematics laureates
Members of the French Academy of Sciences
Members of the Norwegian Academy of Science and Letters
Members of the Royal Netherlands Academy of Arts and Sciences
Foreign Members of the Russian Academy of Sciences
Fellows of the American Mathematical Society
Institute for Advanced Study visiting scholars
Members of the American Philosophical Society
Members of the Royal Swedish Academy of Sciences
Research directors of the French National Centre for Scientific Research