Correspondance de Langlands locale $p$-adique et anneaux de Kisin
Volume 208 / 2023
Acta Arithmetica 208 (2023), 101-126
MSC: Primary 11Sxx; Secondary 11F85.
DOI: 10.4064/aa220520-24-4
Published online: 28 June 2023
Abstract
We use a ${\cal B}$-adic completion and the $p$-adic local Langlands correspondence for ${\rm GL}_2({\bf Q}_p)$ to give a construction of Kisin’s rings and the attached universal Galois representations (in dimension $2$ and for ${\bf Q}_p$) directly from the classical Langlands correspondence. This yields, in particular, a uniform proof of the geometric Breuil–Mézard conjecture in the supercuspidal case.
