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Mathematics > Algebraic Topology
Title: Branched Covering and Profinite Completion
(Submitted on 11 Sep 2023)
Abstract: Artin-Mazur established the \'etale homotopy theory of schemes and proved the generalized Riemann existence theorem, i.e., all \'etale morphisms of a complex finite type scheme induce its profinite completion. We generalize it to piecewise linear pseudomanifolds and prove that all branched coverings of a pseudomanifold induce its profinite completion.
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