Pierre Colmez

Pierre Colmez (born 1962) is a French mathematician and directeur de recherche at the CNRS (IMJ-PRG) known for his work in number theory and p-adic analysis.

Pierre Colmez
Born	1962 (age 62–63)
Nationality	French
Alma mater	École Normale Supérieure University of Grenoble.
Children	Coralie Colmez
Awards	Fermat Prize (2005)
Scientific career
Fields	Mathematics
Institutions	CNRS Sorbonne University
Doctoral advisor	John H. Coates Jean-Marc Fontaine

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 ${\displaystyle p}$-adic representations of ${\displaystyle p}$-adic groups at the meeting point of Fontaine's and Langlands' programs. His contributions include:

• A proof of a ${\displaystyle p}$-adic analog of Dirichlet's analytic class number formula.^[1]
• A conjecture: the Colmez 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.^[2]
• A proof of Perrin-Riou's conjectural explicit reciprocity law related to the functional equation of ${\displaystyle p}$-adic L-functions.^[3]
• 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 "weakly admissible implies admissible"^[4] and the "${\displaystyle p}$-adic monodromy conjecture" which describe representations coming from geometry, or the overconvergence of all representations,^[5][6] and the addition of new concepts such as "trianguline representations"^[7] or "Banach-Colmez spaces".^[8][9]
• A construction 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 "Colmez's Montreal functor"^[10]) from representation of ${\displaystyle \mathrm {GL} _{2}(\mathbb {Q} _{p})}$ to representations of the absolute Galois group of ${\displaystyle \mathbb {Q} _{p}}$.^[11]
• Comparison theorems for ${\displaystyle p}$-adic algebraic and analytic varieties with applications to a geometrization of the ${\displaystyle p}$-adic local Langlands correspondence.^[12][13][14]

With Jean-Pierre Serre, he co-edited the Correspondance Grothendieck-Serre (2001)^[15][16] and the Correspondance Serre-Tate (2015).^[17]

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.^[18]

Colmez has won the French Go championship four times.^[19]

Personal life

Pierre Colmez and Leila Schneps are the parents of Coralie Colmez.^[20][21] Violinist David Grimal is Colmez's first cousin.

External links

• Pierre Colmez' website
• Pierre Colmez at the Mathematics Genealogy Project