English

Locally cyclic extensions with Galois group $GL_2(p)$

Number Theory 2023-10-05 v2

Abstract

Using Galois representations attached to elliptic curves, we construct Galois extensions of Q\mathbb{Q} with group GL2(p)GL_2(p) in which all decomposition groups are cyclic. This is the first such realization for all primes pp.

Keywords

Cite

@article{arxiv.2209.08293,
  title  = {Locally cyclic extensions with Galois group $GL_2(p)$},
  author = {Sara Arias-de-Reyna and Joachim König},
  journal= {arXiv preprint arXiv:2209.08293},
  year   = {2023}
}

Comments

15 pages. Section 5 is now merged with section 4 according to the suggestion of the referee. To appear in Int. J. Number Theory

R2 v1 2026-06-28T01:29:48.061Z