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arXiv · 1609.06902

Patching and the p-adic Langlands program for GL(2, Q_p)

Ana Caraiani·Matthew Emerton·Toby Gee·David Geraghty·Vytautas Paskunas·Sug Woo Shin
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Abstract

We present a new construction of the p-adic local Langlands correspondence for GL(2, 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 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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Ana Caraiani, Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paskunas, Sug Woo Shin. 2016-09-22. Patching and the p-adic Langlands program for GL(2, Q_p). https://doi.org/10.1112/s0010437x17007606

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