Pierre Colmez

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Pierre Colmez
Pierre Colmez (cropped).jpg
Born1962 (age 60–61)
Alma materÉcole Normale Supérieure and Grenoble University
ChildrenCoralie Colmez
AwardsFermat Prize (2005)
Scientific career
InstitutionsParis VI University
Doctoral advisorJohn H. Coates
Jean-Marc Fontaine

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 contributions to the study of L-functions and p-adic Galois representations.

In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin.[1] With Jean-Pierre Serre he edited the Correspondance Grothendieck-Serre (2001).[2][3]

Colmez has won the French Go championship four times.[4]

Mathematical work[edit]

He works on special values of L-functions and -adic representations of -adic groups at the meeting point of Fontaine's and Langlands' programs. His contributions include:

  • A proof[5] of a -adic analog of Dirichlet's analytic class number formula.
  • A conjecture[6] "Colmez's conjecture" relating Artin L-functions at and periods of abelian varieties with complex multiplication, a far reaching generalization of the Chowla-Selberg formula.
  • A proof[7] of Perrin-Riou's conjectural explicit reciprocity law related to the functional equation of -adic L-functions.
  • Several contributions to Fontaine's program of classification of -adic representations of the absolute Galois group of a finite extension of , including proofs of conjectures of Fontaine such as[8] "weakly admissible implies admissible" and the[9] "-adic monodromy conjecture" which describe representations coming from geometry, or the overconvergence of all representations,[10] and addition of new concepts such as[11] "trianguline representations" or[12] "Banach-Colmez[13] spaces".
  • A construction[14] of the -adic local Langlands correspondence for , via the construction of a functor (known as "Colmez's functor" or[15] "Colmez's Montreal functor") from representation of to representations of the absolute Galois group of .
  • Comparison theorems[16] · [17] · [18] for -adic algebraic and analytic varieties with applications to a geometrization of the -adic local Langlands correspondence.

Personal life[edit]

Pierre Colmez and Leila Schneps are the parents of Coralie Colmez.[19][20] Violinist David Grimal is Colmez's first cousin.

External links[edit]


  1. ^ Colmez, Pierre (1998). "Représentations p-adiques d'un corps local". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 153–162.
  2. ^ Raynaud, Michel (October 2003). "Book Review: Correspondance Grothendieck-Serre " (PDF). Notices of the AMS. 50 (9): 1085–1086.
  3. ^ Colmez, P.; Serre, J.-P., eds. (2004). Grothendieck-Serre Correspondence. American Mathematical Society; Société Mathématique de France. ISBN 978-0-8218-3424-4; bilingual edition{{cite book}}: CS1 maint: postscript (link)
  4. ^ Open - Fédération Française de Go - Jeu de go
  5. ^ Résidu en s=1 des fonctions zêta p-adiques, Inventiones mathematicae 91 (1988), 371-389
  6. ^ Périodes des variétés abéliennes à multiplication complexe, Annals of Mathematics 138 (1993), 625–683
  7. ^ Théorie d'Iwasawa des représentations de de Rham d'un corps local, Annals of Mathematics 148 (1998), 485–571
  8. ^ Construction des représentations p-adiques semi-stables (avec J.-M. Fontaine), Inventiones mathematicae 140 (2000), 1–43 (avec Jean-Marc Fontaine)
  9. ^ Espaces Vectoriels de dimension finie et représentations de de Rham, Astérisque 319 (2008), 117–186
  10. ^ Représentations p-adiques surconvergentes, Inventiones mathematicae 133 (1998), 581–611 (avec Frédéric Cherbonnier)
  11. ^ Représentations triangulines de dimension 2, Astérisque 319 (2008), 213–258
  12. ^ Espaces de Banach de dimension finie, Journal Institut de Mathématiques de Jussieu 1 (2002), 331–439
  13. ^ Arthur-César Le Bras, Espaces de Banach–Colmez et faisceaux cohérents sur la courbe de Fargues–Fontaine, Duke Math. J. 167 (2018), 3455-3532
  14. ^ Représentations de et -modules, Astérisque 330 (2010), 281–509
  15. ^ Vytautas Paškūnas, The image of Colmez’s Montreal functor, Publications mathématiques de l'IHÉS 118 (2013), 1–191
  16. ^ -adic vanishing cycles and syntomic cohomology, Inventiones mathematicae 208 (2017), 1-108 (with Wiesława Nizioł).
  17. ^ Cohomologie -adique de la tour de Drinfeld, le cas de la dimension 1, Journal of the AMS 33 (2020), 311–362 (with Wiesława Nizioł and Gabriel Dospinescu).
  18. ^ Cohomology of -adic Stein spaces, Inventiones mathematicae 219 (2020), 873–985 (with Wiesława Nizioł and Gabriel Dospinescu).
  19. ^ "Allow me to explain, Your Honour". The Economist. 2 May 2013. Retrieved 2 October 2020.
  20. ^ Tsui, Diana (9 January 2018). "The Mathematician Who Moonlights As a Rock-Band Violinist". The Cut. Retrieved 2 October 2020.