Patching and the -adic Langlands program for

We present a new construction of the $p$ -adic local Langlands correspondence for $\operatorname{GL}_{2}(\mathbb{Q}_{p})$ via the patching method of Taylor–Wiles and Kisin. This construction sheds light on the relationship between the various other approaches to both the local and the global aspects...

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Veröffentlicht in:Compositio mathematica 2018-03, Vol.154 (3), p.503-548
Hauptverfasser: Caraiani, Ana, Emerton, Matthew, Gee, Toby, Geraghty, David, Paškūnas, Vytautas, Shin, Sug Woo
Format: Artikel
Sprache:eng ; fre
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Zusammenfassung:We present a new construction of the $p$ -adic local Langlands correspondence for $\operatorname{GL}_{2}(\mathbb{Q}_{p})$ via the patching method of Taylor–Wiles and Kisin. This construction sheds light on the relationship between the various other approaches to both the local and the global aspects of the $p$ -adic Langlands program; in particular, it gives a new proof of many cases of the second author’s local–global compatibility theorem and relaxes a hypothesis on the local mod  $p$ representation in that theorem.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X17007606