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Patching and the \(p\)-adic local Langlands correspondence. (English) Zbl 1403.11073

Summary: We use the patching method of Taylor-Wiles and Kisin to construct a candidate for the \(p\)-adic local Langlands correspondence for \(\mathrm{GL}_n (F)\), \(F\) a finite extension of \(\mathbb{Q}_p\). We use our construction to prove many new cases of the Breuil-Schneider conjecture.

MSC:

11S37 Langlands-Weil conjectures, nonabelian class field theory
22E50 Representations of Lie and linear algebraic groups over local fields
11F85 \(p\)-adic theory, local fields
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