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Generic local deformation rings when l≠p

Shotton, Jack (2022) 'Generic local deformation rings when l≠p.', Compositio Mathematica, 158 (4). pp. 721-749.


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.

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Publisher statement:This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original article is properly cited. Compositio Mathematica is © Foundation Compositio Mathematica.
Date accepted:18 November 2021
Date deposited:26 July 2022
Date of first online publication:03 June 2022
Date first made open access:26 July 2022

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