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arXiv · 2007.13397

Generic local deformation rings when $l \neq p$

Jack Shotton
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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 $l \neq p$, 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 $l \neq p$ Breuil--M\'{e}zard conjecture of the author, in the tame case.

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Jack Shotton. 2020-07-27. Generic local deformation rings when $l \neq p$. https://doi.org/10.1112/s0010437x22007461

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