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On the Geometry of $p$-Typical Covers in Characteristic $p$

Open Access article
 Printed: Feb 2008
  • Kiran S. Kedlaya
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For $p$ a prime, a $p$-typical cover of a connected scheme on which $p=0$ is a finite \'etale cover whose monodromy group (\emph{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 $p$\nobreakdash-typi\-cal quotients of the \'etale fundamental groups, and a decomposition theorem for $p$-typical covers of polynomial rings over an algebraically closed field.
MSC Classifications: 14F35 show english descriptions Homotopy theory; fundamental groups [See also 14H30] 14F35 - Homotopy theory; fundamental groups [See also 14H30]

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