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arXiv · 1309.1600

Local deformation rings and a Breuil-M\'{e}zard conjecture when l\neq p

Jack Shotton
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Abstract

We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd) an analogue of the Breuil-M\'{e}zard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL_2(O_F).

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Jack Shotton. 2013-09-06. Local deformation rings and a Breuil-M\'{e}zard conjecture when l\neq p. https://doi.org/10.2140/ant.2016.10.1437

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