Langlands本地匹配$P$-Adiqueet Kisin戒指

IF 0.5 3区数学 Q3 MATHEMATICS

Acta Arithmetica Pub Date : 2022-04-24 DOI:10.4064/aa220520-24-4

P. Colmez, Gabriel Dospinescu, Wiesława Nizioł

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引用次数: 0

摘要

我们使用${\mathrm｛GL｝｝_2（｛\mathbf Q｝_p）$的${\math cal B｝$adic完备和$p$adic局部Langlands对应关系，直接从经典Langlands相应关系中给出Kisin环的构造和所附的通用Galois表示（在维度2中和对于${\mathebf Q}_p$）。这特别给出了在超悬铃木情况下几何Breuil-M’zard猜想的统一证明。

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

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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