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 |
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Hauptverfasser: | , , , , , |
Format: | Artikel |
Sprache: | eng ; fre |
Schlagworte: | |
Online-Zugang: | Volltext |
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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. |
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ISSN: | 0010-437X 1570-5846 |
DOI: | 10.1112/S0010437X17007606 |