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 conjecture[6] "Colmez's 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[7] 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[8] "weakly admissible implies admissible" and the[9] "-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 -adic local Langlands correspondence for , via the construction of a functor (known as "Colmez's functor" or[15] "Colmez's Montreal functor") from representation of to representations of the absolute Galois group of .
Comparison theorems[16]·[17]·[18] for -adic algebraic and analytic varieties with applications to a geometrization of the -adic local Langlands correspondence.
^Cohomologie -adique de la tour de Drinfeld, le cas de la dimension 1, Journal of the AMS 33 (2020), 311–362 (with Wiesława Nizioł and Gabriel Dospinescu).
^Cohomology of -adic Stein spaces, Inventiones mathematicae 219 (2020), 873–985 (with Wiesława Nizioł and Gabriel Dospinescu).
^"Allow me to explain, Your Honour". The Economist. 2 May 2013. Retrieved 2 October 2020.
^Tsui, Diana (9 January 2018). "The Mathematician Who Moonlights As a Rock-Band Violinist". The Cut. Retrieved 2 October 2020.
May 04, 2024
pierre, colmez, born, 1962, french, mathematician, notable, work, adic, analysis, born1962, nationalityfrenchalma, materÉcole, normale, supérieure, grenoble, universitychildrencoralie, colmezawardsfermat, prize, 2005, scientific, careerfieldsmathematicsinstitu. Pierre Colmez born 1962 is a French mathematician notable for his work on p adic analysis Pierre ColmezBorn1962 age 61 62 NationalityFrenchAlma materEcole Normale Superieure and Grenoble UniversityChildrenCoralie ColmezAwardsFermat Prize 2005 Scientific careerFieldsMathematicsInstitutionsParis VI UniversityDoctoral advisorJohn H CoatesJean Marc Fontaine Colmez studied at Ecole Normale Superieure 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 Contents 1 Mathematical work 2 Personal life 3 External links 4 ReferencesMathematical work editHe works on special values of L functions and p displaystyle p nbsp adic representations of p displaystyle p nbsp adic groups at the meeting point of Fontaine s and Langlands programs His contributions include A proof 5 of a p displaystyle p nbsp adic analog of Dirichlet s analytic class number formula A conjecture 6 Colmez s conjecture relating Artin L functions at s 0 displaystyle s 0 nbsp 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 p displaystyle p nbsp adic L functions Several contributions to Fontaine s program of classification of p displaystyle p nbsp adic representations of the absolute Galois group of a finite extension of Q p displaystyle mathbb Q p nbsp including proofs of conjectures of Fontaine such as 8 weakly admissible implies admissible and the 9 p displaystyle p nbsp 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 p displaystyle p nbsp adic local Langlands correspondence for G L 2 Q p displaystyle mathrm GL 2 mathbb Q p nbsp via the construction of a functor known as Colmez s functor or 15 Colmez s Montreal functor from representation of G L 2 Q p displaystyle mathrm GL 2 mathbb Q p nbsp to representations of the absolute Galois group of Q p displaystyle mathbb Q p nbsp Comparison theorems 16 17 18 for p displaystyle p nbsp adic algebraic and analytic varieties with applications to a geometrization of the p displaystyle p nbsp adic local Langlands correspondence Personal life editPierre Colmez and Leila Schneps are the parents of Coralie Colmez 19 20 Violinist David Grimal is Colmez s first cousin External links editPierre Colmez website Pierre Colmez at the Mathematics Genealogy ProjectReferences edit Colmez Pierre 1998 Representations p adiques d un corps local Doc Math Bielefeld Extra Vol ICM Berlin 1998 vol II pp 153 162 Raynaud Michel October 2003 Book Review Correspondance Grothendieck Serre PDF Notices of the AMS 50 9 1085 1086 Colmez P Serre J P eds 2004 Grothendieck Serre Correspondence American Mathematical Society Societe Mathematique de France ISBN 978 0 8218 3424 4 bilingual edition a href Template Cite book html title Template Cite book cite book a CS1 maint postscript link Open Federation Francaise de Go Jeu de go Residu en s 1 des fonctions zeta p adiques Inventiones mathematicae 91 1988 371 389 Periodes des varietes abeliennes a multiplication complexe Annals of Mathematics 138 1993 625 683 Theorie d Iwasawa des representations de de Rham d un corps local Annals of Mathematics 148 1998 485 571 Construction des representations p adiques semi stables avec J M Fontaine Inventiones mathematicae 140 2000 1 43 avec Jean Marc Fontaine Espaces Vectoriels de dimension finie et representations de de Rham Asterisque 319 2008 117 186 Representations p adiques surconvergentes Inventiones mathematicae 133 1998 581 611 avec Frederic Cherbonnier Representations triangulines de dimension 2 Asterisque 319 2008 213 258 Espaces de Banach de dimension finie Journal Institut de Mathematiques de Jussieu 1 2002 331 439 Arthur Cesar Le Bras Espaces de Banach Colmez et faisceaux coherents sur la courbe de Fargues Fontaine Duke Math J 167 2018 3455 3532 Representations de G L 2 Q p displaystyle mathrm GL 2 mathbb Q p nbsp et f G displaystyle varphi Gamma nbsp modules Asterisque 330 2010 281 509 Vytautas Paskunas The image of Colmez s Montreal functor Publications mathematiques de l IHES 118 2013 1 191 p displaystyle p nbsp adic vanishing cycles and syntomic cohomology Inventiones mathematicae 208 2017 1 108 with Wieslawa Niziol Cohomologie p displaystyle p nbsp adique de la tour de Drinfeld le cas de la dimension 1 Journal of the AMS 33 2020 311 362 with Wieslawa Niziol and Gabriel Dospinescu Cohomology of p displaystyle p nbsp adic Stein spaces Inventiones mathematicae 219 2020 873 985 with Wieslawa Niziol and Gabriel Dospinescu Allow me to explain Your Honour The Economist 2 May 2013 Retrieved 2 October 2020 Tsui Diana 9 January 2018 The Mathematician Who Moonlights As a Rock Band Violinist The Cut Retrieved 2 October 2020 Retrieved from https en wikipedia org w index php title Pierre Colmez amp oldid 1211148151, wikipedia, wiki, book, books, library,
