Prime to p Fundamental Groups, and Tame Galois Actions


Mark Kisin


Research Report 98-12
Date: 30 April 1998


We show that for a local, discretely valued field F with residue characteristic p and a variety U over F, the map from the absolute Galois group of F to the outer automorphisms of the prime to p geometric etale fundamental group of U maps the wild inertia onto a finite image. We show that under favourable conditions this map depends only on the reduction of U modulo a power of the maximal ideal of F.

Key phrases

etale fundamental group. logarithmic structure.

AMS Subject Classification (1991)

Primary: 14G20


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