Locally cyclic extensions with Galois group $G{L}_2(p)$

Abstract

Using Galois representations attached to elliptic curves, we construct Galois extensions of $\mathbb{Q}$ with group $G{L}_2(p)$ in which all decomposition groups are cyclic. This is the first such realization for all primes $p$.

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