Generic local deformation rings when $l \neq p$

27 Jul 2020  ·  Shotton Jack ·

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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Number Theory Representation Theory