Israel Journal of Mathematics

, 118:317 | Cite as

Embedding problems with local conditions

  • David Harbater


LetY→X be a connectedG-Galois cover of affine varieties in characteristicp, and supposeG=Γ/P for somep-groupP. We show that there is a connected Γ-Galois coverZ→X dominatingY→X, and thatZ→X can be chosen to have prescribed behavior over a given closed subset ofX. There are several versions of this result, depending on whether ramification is permitted, and whether adelic behavior is prescribed. The results are deduced from a general assertion about embedding problems, which is proven for profinite groups.


Weak Solution Exact Sequence Fundamental Group Galois Group Finite Type 
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Copyright information

© Hebrew University 2000

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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