On 2-dimensional 2-adic Galois representations of local and global fields

被引：15

作者：

Paskunas, Vytautas ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fak Math, Thea Leymann Str 9, D-45127 Essen, Germany

来源：

ALGEBRA & NUMBER THEORY | 2016年 / 10卷 / 06期

关键词：

p-adic Langlands; Fontaine-Mazur; modularity lifting; MOD P REPRESENTATIONS; MODULAR-REPRESENTATIONS; GL(2)(Q(P)); CONJECTURE; SPACE;

D O I：

10.2140/ant.2016.10.1301

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the generic blocks in the category of smooth locally admissible mod-2 representations of GL(2) (Q(2)). As an application we obtain new cases of the Breuil-Mezard and Fontaine-Mazur conjectures for 2-dimensional 2-adic Galois representations.

引用

页码：1301 / 1358

页数：58

共 50 条

[1] On the modularity of certain 2-adic Galois representations
Dickinson, M
DUKE MATHEMATICAL JOURNAL, 2001, 109 (02) : 319 - 382
[2] Modularity of nearly ordinary 2-adic residually dihedral Galois representations
Allen, Patrick B.
COMPOSITIO MATHEMATICA, 2014, 150 (08) : 1235 - 1346
[3] Genetic Code and Deformation of the 2-Dimensional 2-Adic Metric
Khrennikov, Andrei Yu
Kozyrev, Sergei, V
P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS, 2011, 3 (02) : 165 - 168
[4] Genetic code and deformation of the 2-dimensional 2-adic metric
Andrei Yu. Khrennikov
Sergei V. Kozyrev
P-Adic Numbers, Ultrametric Analysis, and Applications, 2011, 3 (2) : 165 - 168
[5] 2-DIMENSIONAL P-ADIC GALOIS REPRESENTATIONS UNRAMIFIED AWAY FROM P
MAZUR, B
COMPOSITIO MATHEMATICA, 1990, 74 (02) : 115 - 133
[6] Octic 2-adic fields
Jones, John W.
Roberts, David P.
JOURNAL OF NUMBER THEORY, 2008, 128 (06) : 1410 - 1429
[7] LOCAL ORTHOGONAL GROUPS OVER 2-ADIC FIELDS .2.
CHANG, CN
JOURNAL OF ALGEBRA, 1974, 30 (1-3) : 421 - 435
[8] GALOIS GROUPS OF DEGREE 12 2-ADIC FIELDS WITH TRIVIAL AUTOMORPHISM GROUP
Awtrey, Chad
Miles, Nicole E.
Shill, Christoper
Strosnider, Erin
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2016, 38 (05): : 457 - 471
[9] LOCAL ORTHOGONAL GROUPS OVER 2-ADIC FIELDS 1
CHANG, C
JOURNAL OF ALGEBRA, 1974, 29 (01) : 57 - 64
[10] SCHUR SUBGROUPS OF 2-ADIC FIELDS
YAMADA, T
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (02): : A250 - A250

← 1 2 3 4 5 →