Unramified Heisenberg group extensions of number fields
arXiv:1912.03019 · doi:10.1007/s11856-021-2260-8
Abstract
We construct étale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic fields that admit everywhere unramified generalized Heisenberg Galois extensions.
11 pages; added Remark 3.4, extended Section 3.3, shortened Section 4.2 and added Section 4.3