Mathematics – Algebraic Geometry
Scientific paper
2010-04-13
Mathematics
Algebraic Geometry
PhD thesis; french
Scientific paper
The tempered fundamental group of a p-adic analytic variety classifies \'etale coverings that become topological coverings (for the Berkovich topology) after finite \'etale base change. I study what can be recovered from the tempered fundamental group. In particular, I prove that, for a Mumford curve, one can recover the metric of the graph of the stable reduction from the tempered fundamental group. I also study how the tempered fundamental group behaves along the fibers of a fibration.
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