$p$-adic Hurwitz numbers

Abstract

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.

arXiv comment14 pages

References in corpus (4)

• Cyclic coverings of the $p$-adic projective line by Mumford curves
• Harmonic morphisms and hyperelliptic graphs
• The j-invariant of a plane tropical cubic
• Analytification is the limit of all tropicalizations