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arXiv · 2204.11217

Correspondance de Langlands locale $p$-adique et anneaux de Kisin

Pierre Colmez·Gabriel Dospinescu·Wiesława Nizioł
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Abstract

We use a ${\mathcal B}$-adic completion and the $p$-adic local Langlands correspondence for ${\mathrm {GL}}_2({\mathbf Q}_p )$ to give a construction of Kisin's rings and the attached universal Galois representations (in dimension 2 and for ${\mathbf Q}_p$) directly from the classical Langlands correspondence. This gives, in particular, a uniform proof of the geometric Breuil-M\'ezard conjecture in the supercuspidal case.

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Pierre Colmez, Gabriel Dospinescu, Wiesława Nizioł. 2022-04-24. Correspondance de Langlands locale $p$-adique et anneaux de Kisin. https://arxiv.org/abs/2204.11217

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