Vol. 12, No. 4, 2018

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

Volume 12
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

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
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Akizuki–Witt maps and Kaletha's global rigid inner forms

Olivier Taïbi

Vol. 12 (2018), No. 4, 833–884
Abstract

We give an explicit construction of global Galois gerbes constructed more abstractly by Kaletha to define global rigid inner forms. This notion is crucial to formulate Arthur’s multiplicity formula for inner forms of quasisplit reductive groups. As a corollary, we show that any global rigid inner form is almost everywhere unramified, and we give an algorithm to compute the resulting local rigid inner forms at all places in a given finite set. This makes global rigid inner forms as explicit as global pure inner forms, up to computations in local and global class field theory.

Keywords
class field theory, Akizuki–Witt, rigid inner forms, global Langlands correspondence, Arthur multiplicity formula
Mathematical Subject Classification 2010
Primary: 11E72
Secondary: 11F55, 11F70, 11F72
Milestones
Received: 17 February 2017
Revised: 28 November 2017
Accepted: 29 December 2017
Published: 11 July 2018
Authors
Olivier Taïbi
CNRS ; Unité de Mathématiques Pures et Appliquées (UMPA)
Ecole Normale Supérieure de Lyon
Lyon
France