Generic local deformation rings when $l \neq p$

Compositio mathematica

article

Jack Shotton¹ 

[1] Department of Mathematical Sciences, Durham University

关键词: Galois representations;    local Langlands correspondence;    Breuil–Mézard conjecture;    11F80;   

DOI  :  10.1112/S0010437X22007461

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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–Mézard conjecture of the author, in the tame case.

【 授权许可】

CC BY