On the geometry of p-typical covers in characteristic p

Details On the geometry of p-typical covers in characteristic p On the geometry of p-typical covers in characteristic p

2005-01-30

arxiv.org/abs/math/0501541v3

Mathematics

Algebraic Geometry

25 pages; v3: refereed version

Scientific paper

A p-typical cover of a connected scheme on which p=0 is a finite etale cover whose monodromy group (i.e., the Galois group of its normal closure) is a p-group. The geometry of such covers exhibits some unexpectedly pleasant behaviors; building on work of Katz, we demonstrate some of these. These include a criterion for when a morphism induces an isomorphism of the p-typical quotients of the etale fundamental groups, and a decomposition theorem for p-typical covers of polynomial rings over an algebraically closed field.

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