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DEFORMATION CONDITIONS FOR PSEUDOREPRESENTATIONS

Part of: Algebraic number theory: local and $p$-adic fields Discontinuous groups and automorphic forms Rings with polynomial identity

Published online by Cambridge University Press:  18 July 2019

PRESTON WAKE Open the ORCID record for PRESTON WAKE [Opens in a new window]  and
CARL WANG-ERICKSON Open the ORCID record for CARL WANG-ERICKSON [Opens in a new window]
PRESTON WAKE
Affiliation:
Institute for Advanced Study, Princeton, NJ 08540, USA; [email protected]
CARL WANG-ERICKSON
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK; [email protected]

Abstract

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Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur’s Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna’s theory to pseudorepresentations.

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 16R99: None of the above, but in this section 11S20: Galois theory
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e20
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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