Pierre Colmez (born 1962) is a French mathematician and directeur de recherche at the CNRS (IMJ-PRG) known for his work in number theory and p-adic analysis.
Education Colmez studied at École Normale Supérieure and obtained his doctorate from the University of Grenoble.
Research 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 of a -adic analog of Dirichlet's analytic class number formula.Résidu en s=1 des fonctions zêta p-adiques, Inventiones mathematicae 91 (1988), 371-389 A conjecture: the Colmez conjecture relating Artin L-functions at and periods of abelian varieties with complex multiplication, a far-reaching generalization of the Chowla-Selberg formula.Périodes des variétés abéliennes à multiplication complexe, Annals of Mathematics 138 (1993), 625–683 A proof of Perrin-Riou's conjectural explicit reciprocity law related to the functional equation of -adic L-functions.Théorie d'Iwasawa des représentations de de Rham d'un corps local, Annals of Mathematics 148 (1998), 485–571 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 "weakly admissible implies admissible"Construction des représentations p-adiques semi-stables (avec J.-M. Fontaine), Inventiones mathematicae 140 (2000), 1–43 (avec Jean-Marc Fontaine) and the "-adic monodromy conjecture" which describe representations coming from geometry, or the overconvergence of all representations,Espaces Vectoriels de dimension finie et représentations de de Rham, Astérisque 319 (2008), 117–186Représentations p-adiques surconvergentes, Inventiones mathematicae 133 (1998), 581–611 (avec Frédéric Cherbonnier) and the addition of new concepts such as "trianguline representations"Représentations triangulines de dimension 2, Astérisque 319 (2008), 213–258 or "Banach-Colmez spaces".Espaces de Banach de dimension finie, Journal Institut de Mathématiques de Jussieu 1 (2002), 331–439Arthur-César Le Bras, Espaces de Banach–Colmez et faisceaux cohérents sur la courbe de Fargues–Fontaine, Duke Math. J. 167 (2018), 3455-3532 A construction of the -adic local Langlands correspondence for , via the construction of a functor (known as "Colmez's functor" or "Colmez's Montreal functor"Vytautas Paškūnas, The image of Colmez’s Montreal functor, Publications mathématiques de l'IHÉS 118 (2013), 1–191) from representation of to representations of the absolute Galois group of .Représentations de et -modules, Astérisque 330 (2010), 281–509 Comparison theorems for -adic algebraic and analytic varieties with applications to a geometrization of the -adic local Langlands correspondence.-adic vanishing cycles and syntomic cohomology, Inventiones mathematicae 208 (2017), 1-108 (with Wiesława Nizioł).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).Cohomology of -adic Stein spaces, Inventiones mathematicae 219 (2020), 873–985 (with Wiesława Nizioł and Gabriel Dospinescu).
With Jean-Pierre Serre, he co-edited the Correspondance Grothendieck-Serre (2001) and the Correspondance Serre-Tate (2015).Documents Mathématiques 13, 14, Société Mathématique de France, 2015
Awards and honors Colmez 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 at the International Congress of Mathematicians in Berlin.
Colmez has won the French Go championship four times.Open - Fédération Française de Go - Jeu de go
Personal life Pierre Colmez and Leila Schneps are the parents of Coralie Colmez. Violinist David Grimal is Colmez's first cousin.
External links Pierre Colmez' website
References