  A weak wild arithmetic quotient singularity arises from the quotient of a
smooth arithmetic surface by a finite group action, where the inertia group of
a point on a closed characteristic p fiber is a p-group acting with smallest
possible ramification jump. In this paper, we give complete explicit
resolutions of these singularities using deformation theory and valuation
theory, taking a more local perspective than previous work has taken. Our
descriptions answer several questions of Lorenzini. Along the way, we give a
valuation-theoretic criterion for a normal snc-model of P^1 over a discretely
valued field to be regular.
