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 $$\mathbb{Q}_p$$, 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 $$\mathrm{GL}_2(\mathbb{Q}_p)$$, via the construction of a functor (known as "Colmez's functor" or "Colmez's Montreal functor") from representation of $$\mathrm{GL}_2(\mathbb{Q}_p)$$ to representations of the absolute Galois group of $$\mathbb{Q}_p$$.
 * 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.