Pierre Colmez
Born	1962 (age 61–62)
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]

Colmez has won the French Go championship four times.^[4]

Mathematical work

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

• A proof^[5] of a ${\displaystyle p}$-adic analog of Dirichlet's analytic class number formula.
• A conjecture^[6] "Colmez's conjecture" relating Artin L-functions at ${\displaystyle s=0}$ 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 ${\displaystyle p}$-adic L-functions.
• Several contributions to Fontaine's program of classification of ${\displaystyle p}$-adic representations of the absolute Galois group of a finite extension of ${\displaystyle \mathbb {Q} _{p))$, including proofs of conjectures of Fontaine such as^[8] "weakly admissible implies admissible" and the^[9] "${\displaystyle p}$-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 ${\displaystyle p}$-adic local Langlands correspondence for ${\displaystyle \mathrm {GL} _{2}(\mathbb {Q} _{p})}$, via the construction of a functor (known as "Colmez's functor" or^[15] "Colmez's Montreal functor") from representation of ${\displaystyle \mathrm {GL} _{2}(\mathbb {Q} _{p})}$ to representations of the absolute Galois group of ${\displaystyle \mathbb {Q} _{p))$.
• Comparison theorems^[16] · ^[17] · ^[18] for ${\displaystyle p}$-adic algebraic and analytic varieties with applications to a geometrization of the ${\displaystyle p}$-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.