The absolute Galois group of a p-adic field

Summary: This article investigates the tame fundamental groups of smooth affine curves, smooth projective varieties, and smooth quasi-projective varieties with good compactification over an algebraically closed field of characteristic p. It shows that the tame fundamental group of a smooth affine curve is a projective profinite group, the fundamental group of a smooth projective variety is finitely presented, and the tame fundamental group of a smooth quasi-projective variety with a good compactification is also finitely presented.