Basepoint dependence of the unipotent fundamental group of P1 Qp {0,1, ∞}

Abstract

Let X be the scheme P1Qp \ {0,1, ∞} We can assign a fundamental group to each rational basepoint on this scheme. These groups are non-canonically isomorphic, so they need not have isomorphic Galois actions. We study a description of this map from points to groups with Galois action, in terms of non-abelian cohomology. Using this description, we see that the fundamental groups associated to di�fferent basepoints are not isomorphic