Jump to ContentJump to Main Navigation
Show Summary Details

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

IMPACT FACTOR increased in 2015: 1.616
5-year IMPACT FACTOR: 1.690
Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

See all formats and pricing
Select Volume and Issue


30,00 € / $42.00 / £23.00

Get Access to Full Text

First steps towards p-adic Langlands functoriality

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2007, Issue 610, Pages 149–180, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2007.070, December 2007

Publication History

Published Online:


By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modification of the classical local Langlands correspondence, we associate with any pair consisting of a Weil-Deligne group representation and a type of a filtration (admissible or not) a specific locally algebraic representation of a general linear group. We advertise the conjecture that this pair comes from a de Rham representation if and only if the corresponding locally algebraic representation carries an invariant norm. In the crystalline case, the Weil-Deligne group representation is unramified and the associated locally algebraic representation can be studied using the classical Satake isomorphism. By extending the latter to a specific norm completion of the Hecke algebra, we show that the existence of an invariant norm implies that our pair, indeed, comes from a crystalline representation. We also show, by using the formalism of Tannakian categories, that this latter fact is compatible with classical unramified Langlands functoriality and therefore generalizes to arbitrary split reductive groups.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Claus Sorensen
Pacific Journal of Mathematics, 2015, Volume 275, Number 1, Page 191
Pierre Colmez and Gabriel Dospinescu
Algebra & Number Theory, 2014, Volume 8, Number 6, Page 1447
Claus Sorensen
Annals of Mathematics, 2013, Volume 177, Number 1, Page 367
Eknath Ghate and Narasimha Kumar
Pacific Journal of Mathematics, 2011, Volume 252, Number 2, Page 379

Comments (0)

Please log in or register to comment.