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On different notions of tameness in arithmetic geometry

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Abstract

The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these definitions are essentially equivalent. Furthermore, we prove finiteness theorems for the tame fundamental groups of arithmetic schemes.

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  1. NWF I-Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Moritz Kerz & Alexander Schmidt

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  1. Moritz Kerz
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  2. Alexander Schmidt
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Correspondence to Alexander Schmidt.

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Kerz, M., Schmidt, A. On different notions of tameness in arithmetic geometry. Math. Ann. 346, 641–668 (2010). https://doi.org/10.1007/s00208-009-0409-6

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  • DOI: https://doi.org/10.1007/s00208-009-0409-6

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