On different notions of tameness in arithmetic geometry

Details On different notions of tameness in arithmetic geometry On different notions of tameness in arithmetic geometry

2008-07-07

arxiv.org/abs/0807.0979v2

Mathematics

Algebraic Geometry

final version, minor changes, 24 pages

Scientific paper

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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