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 with group in which all decomposition groups are cyclic. This is the first such realization for all primes .
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