Constructing Galois representations ramified at one prime

JOURNAL OF NUMBER THEORY

卷:222

Article

Ray, Anwesh¹ 

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

关键词: Deformations of Galois representations;   

DOI  :  10.1016/j.jnt.2020.12.005

来源: Elsevier

【 摘 要 】

Let n > 1, e >= 0 and a prime number p >= 2(n+2+2e) + 3, such that the index of regularity of p is <= e. We show that there are infinitely many irreducible Galois representations rho : Gal((Q) over bar /Q) -> GL(n) (Q(p)) unramified at all primes l not equal p. Furthermore, these representations are shown to have image containing a fixed finite index subgroup of SLn (Z(p)). Such representations are constructed by lifting suitable residual representations (rho) over bar with image in the diagonal torus in GL(n) (F-p), for which the global deformation problem is unobstructed. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free