Etale covers and local fundamental groups.

Etale covers and local fundamental groups.

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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.