2023/10/11 by Iorga, Andreea
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2310.07105
In this paper, we prove, under a technical assumption, that any semi-direct product of a p-group G with a group Φ of order prime to p can appear as the Galois group of a tower of extensions H/K/F with the property that H is the maximal pro-p extension of K that is unramified everywhere, and Gal(H/K) = G. A consequence of this result is that any local ring admitting a surjection to ℤ5 or ℤ7 with finite kernel can occur as a universal everywhere unramified deformation ring.