Abstract
We compute the deformation rings of two dimensional mod representations of with fixed inertial type for an odd prime, a prime distinct from , and a finite extension. We show that in this setting an analogue of the Breuil–Mézard conjecture holds, relating the special fibres of these deformation rings to the mod reduction of certain irreducible representations of .
Citation
Jack Shotton. "Local deformation rings for $\operatorname{GL}_2$ and a Breuil–Mézard conjecture when $l \neq p$." Algebra Number Theory 10 (7) 1437 - 1475, 2016. https://doi.org/10.2140/ant.2016.10.1437
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