Patching and the -adic Langlands program for

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
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Patching
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container_issue 3
container_start_page 503
container_title Compositio mathematica
container_volume 154
creator Caraiani, Ana
Emerton, Matthew
Gee, Toby
Geraghty, David
Paškūnas, Vytautas
Shin, Sug Woo
description 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.
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title Patching and the -adic Langlands program for
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