Caraiani, Ana; Emerton, Matthew; Gee, Toby; Geraghty, David; Paškūnas, Vytautas; Shin, Sug Woo Patching and the \(p\)-adic local Langlands correspondence. (English) Zbl 1403.11073 Camb. J. Math. 4, No. 2, 197-287 (2016). 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. Cited in 7 ReviewsCited in 54 Documents 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 Keywords:\(p\)-adic local Langlands correspondence; Breuil-Schneider conjecture PDFBibTeX XMLCite \textit{A. Caraiani} et al., Camb. J. Math. 4, No. 2, 197--287 (2016; Zbl 1403.11073) Full Text: DOI arXiv