Pierre Colmez

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. With Jean-Pierre Serre he edited the ''Correspondance Grothendieck-Serre '' (2001).

Colmez has won the French Go championship four times.

Mathematical work

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

* A proof of a $p$-adic analog of Dirichlet's analytic class number formula.
* A conjecture "Colmez's conjecture" relating Artin L-functions at $s=0$ 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 $p$-adic L-functions.
* Several contributions to Fontaine's program of classification of $p$-adic representations of the absolute Galois group of a finite extension of $\mathbb_p$, including proofs of conjectures of Fontaine such as "weakly admissible implies admissible" and the "$p$-adic monodromy conjecture" which describe representations coming from geometry, or the overconvergence of all representations, and addition of new concepts such as "trianguline representations" or "Banach-Colmez spaces".
* A construction of the $p$-adic local Langlands correspondence for $\mathrm_2(\mathbb_p)$, via the construction of a functor (known as "Colmez's functor" or "Colmez's Montreal functor") from representation of $\mathrm_2(\mathbb_p)$ to representations of the absolute Galois group of $\mathbb_p$.
* Comparison theorems for $p$-adic algebraic and analytic varieties with applications to a geometrization of the $p$-adic local Langlands correspondence.

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

{{DEFAULTSORT:Colmez, Pierre
Living people
École Normale Supérieure alumni
20th-century French mathematicians
21st-century French mathematicians
University of Paris alumni
1962 births
French Go players
Arithmetic geometers