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Generic local deformation rings when l≠p

Shotton, Jack

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Abstract

We determine the local deformation rings of sufficiently generic mod l representations of the Galois group of a p-adic field, when l≠p, relating them to the space of q-power-stable semisimple conjugacy classes in the dual group. As a consequence, we give a local proof of the l≠p Breuil–Mézard conjecture of the author, in the tame case.

Citation

Shotton, J. (2022). Generic local deformation rings when l≠p. Compositio Mathematica, 158(4), 721-749. https://doi.org/10.1112/s0010437x22007461

Journal Article Type Article
Acceptance Date Nov 18, 2021
Online Publication Date Jun 3, 2022
Publication Date 2022-04
Deposit Date Jul 26, 2022
Publicly Available Date Jul 26, 2022
Journal Compositio Mathematica
Print ISSN 0010-437X
Electronic ISSN 1570-5846
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 158
Issue 4
Pages 721-749
DOI https://doi.org/10.1112/s0010437x22007461
Public URL https://durham-repository.worktribe.com/output/1199431

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
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 article is properly cited. Compositio Mathematica is © Foundation Compositio Mathematica.





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