The Local Langlands Correspondence for GLn over p-adic fields

被引：0
|
作者：
Peter Scholze
机构：
[1] Mathematisches Institut der Universität Bonn,
来源：
Inventiones mathematicae | 2013年 / 192卷
关键词：
Grothendieck Group; Compact Open Subgroup; Universal Deformation; Shimura Variety; Supercuspidal Representation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We extend our methods from Scholze (Invent. Math. 2012, doi:10.1007/s00222-012-0419-y) to reprove the Local Langlands Correspondence for GLn over p-adic fields as well as the existence of ℓ-adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for which we prove a local-global compatibility statement as in the book of Harris-Taylor (The Geometry and Cohomology of Some Simple Shimura Varieties, 2001).
引用
收藏
页码：663 / 715
页数：52
相关论文
共 50 条
  • [1] The Local Langlands Correspondence for GLn over p-adic fields
    Scholze, Peter
    INVENTIONES MATHEMATICAE, 2013, 192 (03) : 663 - 715
  • [2] Patching and the p-adic local Langlands correspondence
    Caraiani, Ana
    Emerton, Matthew
    Gee, Toby
    Geraghty, David
    Paskunas, Vytautas
    Shin, Sug Woo
    CAMBRIDGE JOURNAL OF MATHEMATICS, 2016, 4 (02) : 197 - 287
  • [3] Local p-adic Langlands correspondence and Kisin rings
    Colmez, Pierre
    Dospinescu, Gabriel
    Niziol, Wieslawa
    ACTA ARITHMETICA, 2023, 208 (02) : 101 - 126
  • [4] The local Langlands correspondence for GLn over function fields
    Li-Huerta, Siyan Daniel
    ALGEBRA & NUMBER THEORY, 2022, 16 (09) : 2119 - 2214
  • [5] The p-adic local Langlands correspondence for GL(2)(Q(p))
    Colmez, Pierre
    Dospinescu, Gabriel
    Paskunas, Vytautas
    CAMBRIDGE JOURNAL OF MATHEMATICS, 2014, 2 (01) : 1 - 47
  • [6] On the p-adic Langlands correspondence for algebraic tori
    Birkbeck, Christopher
    JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2020, 32 (01): : 133 - 158
  • [7] PRINCIPAL SERIES OF GLN OVER P-ADIC FIELDS
    HOWE, RE
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 177 (MAR) : 275 - 286
  • [8] CORRESPONDENCE OF LANGLANDS LOCAL p-ADIC FOR GL2 (Qp)
    Berger, Laurent
    ASTERISQUE, 2011, (339) : 157 - 180
  • [9] Correspondence of the Jacquet-Langlands p-adic forms
    Chenevier, G
    DUKE MATHEMATICAL JOURNAL, 2005, 126 (01) : 161 - 194
  • [10] A report on the proof of the Langlands conjectures for GL(N) over p-adic fields
    Henniart, G
    CURRENT DEVELOPMENTS IN MATHEMATICS 1999, 1999, : 55 - 68
12345