$p$-adic Hurwitz numbers

Details $p$-adic Hurwitz numbers $p$-adic Hurwitz numbers

2008-06-04

arxiv.org/abs/0806.0836v2

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We introduce stable tropical curves and use these to count covers of the
$p$-adic projective line of fixed degree and ramification types by Mumford
curves in terms of tropical Hurwitz numbers. Our counts depend on the branch
loci of the covers.

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