A user's guide to the local arithmetic of hyperelliptic curves
Abstract
A new approach has been recently developed to study the arithmetic of hyperelliptic curves y2=f(x) over local fields of odd residue characteristic via combinatorial data associated to the roots of f. Since its introduction, numerous papers have used this machinery of "cluster pictures" to compute a plethora of arithmetic invariants associated to these curves. The purpose of this user's guide is to summarise and centralise all of these results in a self-contained fashion, complemented by an abundance of examples.
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