Vol. 12, No. 4, 2018

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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

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.

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