Globally realizable components of local deformation rings
Number Theory
2023-06-22 v3
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".
Keywords
Cite
@article{arxiv.1807.03529,
title = {Globally realizable components of local deformation rings},
author = {Frank Calegari and Matthew Emerton and Toby Gee},
journal= {arXiv preprint arXiv:1807.03529},
year = {2023}
}
Comments
66 pages; final version, to appear in Journal de l'Institut de Math\'ematiques de Jussieu