Extension of solvable coverings across horizontal divisors over the integers

Source abstract

We study the effect of deleting a horizontal divisor from an arithmetic scheme on its étale fundamental group. Assume that the scheme is regular along the divisor, that each prime component contains a normal crossings point of residue characteristic $2$, and that the generic fibers of the boundary components remain geometrically integral after finite étale base change. We prove that the kernel of the induced surjection on fundamental groups is topologically perfect. In particular, the inclusion induces an isomorphism on maximal prosolvable quotients. We apply this result to projective hyperplane complements and to the extension of representations over complete local coefficient rings.