Jeffrey.YeltonAffiliation: Wesleyan University Title Of Talk: Non-archimedean uniformization of superelliptic curves
URLS: Abstract: Let K be a field with a discrete valuation, and let C be a superelliptic curve given by an equation of the form $y^p = f(x)$ for some prime $p$. The arithmetic of such a curve can be understood in terms of its ramification points, which correspond to roots of the polynomial $f$. In particular, a lot of arithmetic information about C is determined from the cluster data of this set of roots (that is, how close different subsets of the roots are to each other under the non-archimedean metric). Certain curves, called Mumford curves, can be uniformized as a subset of the projective line over K modulo a group of fractional linear transformations. I will demonstrate an explicit way to view the uniformization of a Mumford superelliptic curve C and discuss its implications for the associated cluster data.
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Last update made Tue Mar 10 21:28:06 CDT 2026.
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