On the Geometry ofp-Typical Covers in Characteristicp

Abstract

AbstractForpa prime, ap-typical cover of a connected scheme on whichp= 0 is a finite étale cover whose monodromy group (i.e.,the Galois group of its normal closure) is ap-group. The geometry of such covers exhibits some unexpectedly pleasant behaviors; building on work of Katz, we demonstrate some of these. These include a criterion for when a morphism induces an isomorphism of thep-typical quotients of the étale fundamental groups, and a decomposition theorem forp-typical covers of polynomial rings over an algebraically closed field.