Vol. 8, No. 7, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Monodromy and local-global compatibility for $l=p$

Ana Caraiani

Vol. 8 (2014), No. 7, 1597–1646

We strengthen the compatibility between local and global Langlands correspondences for GLn when n is even and l = p. Let L be a CM field and Π a cuspidal automorphic representation of GLn(AL) which is conjugate self-dual and regular algebraic. In this case, there is an l-adic Galois representation associated to Π, which is known to be compatible with local Langlands in almost all cases when l = p by recent work of Barnet-Lamb, Gee, Geraghty and Taylor. The compatibility was proved only up to semisimplification unless Π has Shin-regular weight. We extend the compatibility to Frobenius semisimplification in all cases by identifying the monodromy operator on the global side. To achieve this, we derive a generalization of Mokrane’s weight spectral sequence for log crystalline cohomology.

Galois representations, automorphic forms, local-global compatibility, monodromy operator, crystalline cohomology
Mathematical Subject Classification 2010
Primary: 11F80
Secondary: 11G18, 11R39
Received: 27 April 2013
Revised: 31 March 2014
Accepted: 18 May 2014
Published: 21 October 2014
Ana Caraiani
Department of Mathematics
Princeton University
Fine Hall
Washington Road
Princeton, NJ 08544
United States