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arXiv · 2007.01749

A user's guide to the local arithmetic of hyperelliptic curves

Alex J. Best·L. Alexander Betts·Matthew Bisatt·Raymond van Bommel·Vladimir Dokchitser·Omri Faraggi·Sabrina Kunzweiler·Céline Maistret·Adam Morgan·Simone Muselli·Sarah Nowell
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Abstract

A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ 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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Alex J. Best, L. Alexander Betts, Matthew Bisatt, Raymond van Bommel, Vladimir Dokchitser, Omri Faraggi, Sabrina Kunzweiler, Céline Maistret, Adam Morgan, Simone Muselli, Sarah Nowell. 2020-07-03. A user's guide to the local arithmetic of hyperelliptic curves. https://arxiv.org/abs/2007.01749

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