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Jean-Pierre Serre: An Overview of His Work

  • Pilar Bayer
Chapter
Part of the The Abel Prize book series (AP)

Abstract

For more than five decades, the mathematical contributions of Jean-Pierre Serre have played an essential role in the development of several areas of mathematics. The present paper aims to provide an overview of his work. The selected references include his books, most of the papers collected in his Œuvres, as well as some of his more recent publications.

Mathematics Subject Classification (2000)

00-02 00A15 01A70 

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References

  1. [Œ]
    Serre, J.-P.: Œuvres, Collected Papers, vol. I (1949–1959), vol. II (1960–1971), vol. III (1972–1984); vol. IV (1985–1998). Springer, Berlin (1986; 2000) Google Scholar
  2. [GACC]
    Serre, J.-P.: Groupes algébriques et corps de classes. Hermann, Paris (1959); 2nd edn. 1975 [translated into English and Russian] zbMATHGoogle Scholar
  3. [CL]
    Serre, J.-P.: Corps locaux. Hermann, Paris (1962); 4th edn. 2004 [translated into English] zbMATHGoogle Scholar
  4. [CG]
    Serre, J.-P.: Cohomologie galoisienne. LNM, vol. 5. Springer, Berlin (1964); 5th edn. revised and completed 1994 [translated into English and Russian] zbMATHGoogle Scholar
  5. [LALG]
    Serre, J.-P.: Lie Algebras and Lie Groups. Benjamin, New York (1965); 2nd edn. LNM, vol. 1500. Springer, Berlin, 1992 [translated into Russian] zbMATHGoogle Scholar
  6. [ALM]
    Serre, J.-P.: Algèbre locale. Multiplicités. LNM, vol. 11. Springer, Berlin (1965); written with the help of P. Gabriel; 3rd edn. 1975 [translated into English and Russian] zbMATHGoogle Scholar
  7. [ALSC]
    Serre, J.-P.: Algèbres de Lie semi-simples complexes. Benjamin, New York (1966) [translated into English and Russian] zbMATHGoogle Scholar
  8. [RLGF]
    Serre, J.-P.: Représentations linéaires des groupes finis. Hermann, Paris (1967) [translated into English, German, Japanese, Polish, Russian and Spanish] zbMATHGoogle Scholar
  9. [McGill]
    Serre, J.-P.: Abelian l-adic Representations and Elliptic Curves. Benjamin, New York (1968), written with the help of W. Kuyk and J. Labute; 2nd edn. A.K. Peters, 1998 [translated into Japanese and Russian] zbMATHGoogle Scholar
  10. [CA]
    Serre, J.-P.: Cours d’arithmétique. Presses Univ. France, Paris (1970); 4th edn. 1995 [translated into Chinese, English, Japanese and Russian] zbMATHGoogle Scholar
  11. [AA]
    Serre, J.-P.: Arbres, amalgames, SL2. Astérisque, vol. 46. Soc. Math. France, Paris (1977), written with the help of H. Bass; 3rd edn. 1983 [translated into English and Russian] zbMATHGoogle Scholar
  12. [MW]
    Serre, J.-P.: Lectures on the Mordell–Weil Theorem. Vieweg, Wiesbaden (1989); 3rd edn. 1997, translated and edited by Martin Brown from notes of M. Waldschmidt. French edition: Publ. Math. Univ. Pierre et Marie Curie, 1984 CrossRefGoogle Scholar
  13. [TGT]
    Serre, J.-P.: Topics in Galois Theory. Jones & Bartlett, Boston (1992), written with the help of H. Darmon; 2nd edn., AK Peters, 2008 zbMATHGoogle Scholar
  14. [SEM]
    Serre, J.-P.: Exposés de séminaires (1950–1999). Documents Mathématiques (Paris), vol. 1. Soc. Math. France, Paris (2001); 2nd edn., augmented, 2008 zbMATHGoogle Scholar
  15. [GRSE]
    Colmez, P., Serre, J.-P. (eds.): Correspondance Grothendieck–Serre. Documents Mathématiques (Paris), vol. 2. Soc. Math. France, Paris (2001); bilingual edn., AMS, 2004 zbMATHGoogle Scholar
  16. [CI]
    Garibaldi, S., Merkurjev, A., Serre, J.-P.: Cohomological Invariants in Galois Cohomology. Univ. Lect. Ser., vol. 28. Am. Math. Soc., Providence (2003) zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Departament d’Àlgebra i Geometria, Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

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