Etale covers and local fundamental groups.

Charlie Stibitz, Princeton University
Fine Hall 322

We look at the problem of when the map on algebraic fundamental groups induced by inclusion of the regular locus into a normal variety is an isomorphism. For each point of the variety, we identify a local obstruction, governed by the local algebraic fundamental group of the point. Finally, we show the equivalence of these obstructions being finite and the existence of a Galois etale cover of the regular locus where the map on fundamental groups is an isomorphism.