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Ramification theory and formal orbifolds in arbitrary dimension. (English) Zbl 1440.14155
Summary: Formal orbifolds are defined in higher dimension to study wild ramification. Their étale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to approximate the étale fundamental groups of normal varieties. Étale site on formal orbifolds are also defined. This framework allows one to study wild ramification in an organized way. Brylinski-Kato filtration, Lefschetz theorem for fundamental groups and \(l\)-adic sheaves in these contexts are also studied.
MSC:
14H30 Coverings of curves, fundamental group
14E22 Ramification problems in algebraic geometry
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