Akizuki–Witt maps and Kaletha’s global rigid inner forms

Taïbi, Olivier

doi:10.2140/ant.2018.12.833

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Akizuki–Witt maps and Kaletha's global rigid inner forms

Olivier Taïbi

Vol. 12 (2018), No. 4, 833–884

DOI: 10.2140/ant.2018.12.833

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

Vol. 12, No. 4, 2018