arXiv subjects
Publications and source records attributed to Frauke Bleher.
We construct \'etale 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.
Let $k$ be an algebraically closed field of characteristic 2, and let $W$ be the ring of infinite Witt vectors over $k$. Suppose $D$ is a dihedral 2-group. We prove that the universal deformation ring $R(D,V)$ of an endo-trivial $kD$-module $V$ is always isomorphic to $W[\mathbb{Z}/2\times\mathbb{Z}/2]$. As a consequence we obtain a similar result for modules $V$ with stable endomorphism ring $k$ belonging to an arbitrary nilpotent block with defect group $D$. This confirms for such $V$ conjectures on the ring structure of the universal deformation ring of $V$ which had previously been shown for $V$ belonging to cyclic blocks or to blocks with Klein four defect groups.