Globally realizable components of local deformation rings
File(s)
Working paper
Author(s)
Calegari, Frank
Emerton, Matthew
Gee, Toby
Type
Working Paper
Abstract
Let n be either 2, or an odd integer greater than 1, and fix a prime p > 2(n
+ 1). Under standard "adequate image" assumptions, we show that the set of
components of n-dimensional p-adic potentially semistable local Galois
deformation rings that are seen by potentially automorphic compatible systems
of polarizable Galois representations over some CM field is independent of the
particular global situation. We also (under the same assumption on n) improve
on the main potential automorphy result of [BLGGT14b], replacing "potentially
diagonalizable" by "potentially globally realizable".
+ 1). Under standard "adequate image" assumptions, we show that the set of
components of n-dimensional p-adic potentially semistable local Galois
deformation rings that are seen by potentially automorphic compatible systems
of polarizable Galois representations over some CM field is independent of the
particular global situation. We also (under the same assumption on n) improve
on the main potential automorphy result of [BLGGT14b], replacing "potentially
diagonalizable" by "potentially globally realizable".
Date Issued
2020-04-04
Citation
2020
Publisher
arXiv
Copyright Statement
© 2020 The Author(s).
Identifier
http://arxiv.org/abs/1807.03529v3
Subjects
math.NT
math.NT
Notes
66 pages; final version, to appear in Journal de l'Institut de Math\'ematiques de Jussieu
Publication Status
Published