Pierre Colmez
Pierre Colmez is a French mathematician and directeur de recherche at the CNRS 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.
- 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.
- A proof 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 "weakly admissible implies admissible" and the "-adic monodromy conjecture" which describe representations coming from geometry, or the overconvergence of all representations, and the addition of new concepts such as "trianguline representations" or "Banach-Colmez spaces".
- A construction of the -adic local Langlands correspondence for, via the construction of a functor from representation of to representations of the absolute Galois group of.
- Comparison theorems for -adic algebraic and analytic varieties with applications to a geometrization of the -adic local Langlands correspondence.
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.