Patching and the p-adic Langlands program for GL2(Qp)

被引：13

作者：

Caraiani, Ana ^{[1
]}

Emerton, Matthew ^{[2
]}

Gee, Toby ^{[1
]}

Geraghty, David ^{[3
]}

Paskunas, Vytautas ^{[4
]}

Shin, Sug Woo ^{[5
,6
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Univ Chicago, Dept Math, 5734 S Univ Ave, Chicago, IL 60637 USA

[3] Boston Coll, Dept Math, 301 Carney Hall, Chestnut Hill, MA 02467 USA

[4] Univ Duisburg Essen, Fak Math, D-45117 Essen, Germany

[5] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[6] Korea Inst Adv Study, 85 Hoegiro, Seoul 130722, South Korea

来源：

COMPOSITIO MATHEMATICA | 2018年 / 154卷 / 03期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

p-adic Langlands; local-global compatibility; Taylor-Wiles patching; MODULAR-REPRESENTATIONS; CONJECTURE;

D O I：

10.1112/S0010437X17007606

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 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.

引用

页码：503 / 548

页数：47

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