# Mathematician:Jean-Pierre Albert Achille Serre

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## Mathematician

French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.

Member of the Bourbaki group.

### Fields Medal

Jean-Pierre Albert Achille Serre was awarded a Fields Medal in $\text {1954}$ at the International Congress of Mathematicians in Amsterdam, Netherlands:

*Achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and extended some of the main results of complex variable theory in terms of sheaves.*

### Wolf Prize

Jean-Pierre Albert Achille Serre was awarded a Wolf Prize for Mathematics in $\text {2000}$:

*For his many fundamental contributions to topology, algebraic geometry, algebra, and number theory and for his inspirational lectures and writing.*

### Abel Prize

Jean-Pierre Albert Achille Serre was awarded an Abel Prize in $\text {2003}$:

*For playing a key role in shaping the modern form of many parts of mathematics, including topology, algebraic geometry and number theory.*

## Nationality

French

## History

- Born: 15 September 1926 in Bages, Pyrénées Orientales, France

## Theorems and Definitions

- Bass-Serre Theory (with Hyman Bass)
- Lyndon-Hochschild-Serre Spectral Sequence (with Roger Conant Lyndon and Gerhard Paul Hochschild)
- Serre Class
- Serre's Conjecture or Serre's Problem, now known as Quillen-Suslin Theorem (for Daniel Gray Quillen and Andrei Suslin)
- Serre's Conjecture concerning Galois Representations
- Serre's Conjecture II concerning Linear Algebraic Groups
- Serre's Criterion (there are several of them)
- Serre Duality
- Serre's FAC
- Serre Fibration
- Serre Group
- Serre's Modularity Conjecture
- Serre's Multiplicity Conjectures
- Serre's Open Image Theorem
- Serre's Property FA
- Serre Relations
- Serre Subcategory
- Serre Functor
- Serre Spectral Sequence
- Serre-Swan Theorem (with Richard Gordon Swan)
- Serre-Tate Theorem (with John Torrence Tate)
- Serre's Theorem in Group Cohomology
- Serre's Theorem on Affineness
- Serre Twist Sheaf
- Serre's Vanishing Theorem
- Thin Set in the Sense of Serre

Results named for **Jean-Pierre Albert Achille Serre** can be found here.

Definitions of concepts named for **Jean-Pierre Albert Achille Serre** can be found here.

## Publications

- 1959:
*Groupes Algébriques et Corps de Classes*- 1988:
*Algebraic Groups and Class Fields*(translation of*Groupes Algébriques et Corps de Classes*from 1959)

- 1988:

- 1962:
*Corps Locaux*- 1980:
*Local Fields*(translation of*Corps Locaux*from 1962)

- 1980:

- 1964:
*Cohomologie Galoisienne*- 1997:
*Galois Cohomology*(translation of*Cohomologie Galoisienne*from 1964)

- 1997:

- 1965:
*Algèbre Locale, Multiplicités*- 2000:
*Local Algebra*(translation of*Algèbre Locale, Multiplicités*from 1965)

- 2000:

- 1965:
*Lie algebras and Lie groups*

- 1966:
*Algèbres de Lie Semi-simples Complexes*- 1987:
*Complex Semisimple Lie Algebras*(translation of*Algèbres de Lie Semi-simples Complexes*from 1966)

- 1987:

- 1968:
*Abelian $\ell$-Adic Representations and Elliptic Curves*

- 1970:
*Cours d'Arithmétique*- 1973:
*A Course in Arithmetic*(translation of*Cours d'Arithmétique*from 1970)

- 1973:

- 1971:
*Représentations Linéaires des Groupes Finis*- 1977:
*Linear Representations of Finite Groups*(translation of*Représentations Linéaires des Groupes Finis*from 1971)

- 1977:

- 1977:
*Arbres, amalgames, SL2*- 1980:
*Trees*(translation of*Arbres, amalgames, SL2*from 1977)

- 1980:

- 1986:
*Oeuvres/Collected Papers*(three volumes) - 1990:
*Lectures on the Mordell-Weil Theorem* - 1992:
*Topics in Galois Theory* - 2000:
*Oeuvres/Collected Papers*(volume IV) - 2003:
*Cohomological Invariants in Galois Cohomology*(with Skip Garibaldi and Alexander Merkurjev) - 2001:
*Exposés de séminaires 1950–1999* - 2003:
*Grothendieck–Serre Correspondence*, bilingual edition, edited with Pierre Colmez - 2012:
*Lectures on $\map {N_X} p$* - 2015:
*Correspondance Serre-Tate*edited with Pierre Colmez - 2016:
*Finite Groups: an Introduction*

## Also known as

Seen reported as **Jean-Pierre Sevre**, but that is probably a mistake.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Jean-Pierre Albert Achille Serre": MacTutor History of Mathematics archive

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Sevre, Jean-Pierre**(1926- )