Algebra & Number Theory

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

Olivier Taïbi

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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.

Article information

Algebra Number Theory, Volume 12, Number 4 (2018), 833-884.

Received: 17 February 2017
Revised: 28 November 2017
Accepted: 29 December 2017
First available in Project Euclid: 28 July 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11E72: Galois cohomology of linear algebraic groups [See also 20G10]
Secondary: 11F55: Other groups and their modular and automorphic forms (several variables) 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F72: Spectral theory; Selberg trace formula

class field theory Akizuki–Witt rigid inner forms global Langlands correspondence Arthur multiplicity formula


Taïbi, Olivier. Akizuki–Witt maps and Kaletha's global rigid inner forms. Algebra Number Theory 12 (2018), no. 4, 833--884. doi:10.2140/ant.2018.12.833.

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