Pierre Colmez
French mathematician
Pierre Colmez
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Born | 1962 (age 60 – 61) |
Nationality | French |
Alma mater | École Normale Supérieure and Grenoble University |
Children | Coralie Colmez |
Awards | Fermat Prize (2005) |
Scientific career | |
Fields | Mathematics |
Institutions | Paris VI University |
Doctoral advisor |
John 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]
Mathematical work
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
Pierre Colmez and Leila Schneps are the parents of Coralie Colmez . [19] [20] Violinist David Grimal is Colmez's first cousin.
External links
References
- ↑ Colmez, Pierre (1998). "Représentations p -adiques d'un corps local" . Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II . pp. 153–162.
- ↑ Raynaud, Michel (October 2003). "Book Review: Correspondance Grothendieck-Serre " (PDF) . Notices of the AMS . 50 (9): 1085–1086.
-
↑
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 ) - ↑ Open - Fédération Française de Go - Jeu de go
- ↑ Résidu en s=1 des fonctions zêta p-adiques, Inventiones mathematicae 91 (1988), 371-389
- ↑ Périodes des variétés abéliennes à multiplication complexe, Annals of Mathematics 138 (1993), 625–683
- ↑ Théorie d'Iwasawa des représentations de de Rham d'un corps local, Annals of Mathematics 148 (1998), 485–571
- ↑ Construction des représentations p-adiques semi-stables (avec J.-M. Fontaine), Inventiones mathematicae 140 (2000), 1–43 (avec Jean-Marc Fontaine )
- ↑ Espaces Vectoriels de dimension finie et représentations de de Rham, Astérisque 319 (2008), 117–186
- ↑ Représentations p-adiques surconvergentes, Inventiones mathematicae 133 (1998), 581–611 (avec Frédéric Cherbonnier)
- ↑ Représentations triangulines de dimension 2, Astérisque 319 (2008), 213–258
- ↑ Espaces de Banach de dimension finie, Journal Institut de Mathématiques de Jussieu 1 (2002), 331–439
- ↑ Arthur-César Le Bras, Espaces de Banach–Colmez et faisceaux cohérents sur la courbe de Fargues–Fontaine, Duke Math. J. 167 (2018), 3455-3532
-
↑
Représentations de
et
-modules, Astérisque 330 (2010), 281–509
- ↑ Vytautas Paškūnas, The image of Colmez’s Montreal functor, Publications mathématiques de l'IHÉS 118 (2013), 1–191
-
↑
-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).
- ↑ "Allow me to explain, Your Honour" . The Economist . 2 May 2013 . Retrieved 2 October 2020 .
- ↑ Tsui, Diana (9 January 2018). "The Mathematician Who Moonlights As a Rock-Band Violinist" . The Cut . Retrieved 2 October 2020 .
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