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

doi:10.1112/blms.12604

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

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Pages (from-to)	825-867
Number of pages	43
Journal	Bulletin of the London Mathematical Society
Volume	54
Issue number	3
Early online date	5 May 2022
DOIs	https://doi.org/10.1112/blms.12604
Publication status	Published - 1 Jun 2022

Bibliographical note

Publisher Copyright:
© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

Keywords

math.NT
11G20 (11G10, 14D10, 14G20, 14H45, 14Q05)

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AU - Bisatt, Matthew

AU - Bommel, Raymond van

AU - Dokchitser, Vladimir

AU - Faraggi, Omri

AU - Kunzweiler, Sabrina

AU - Maistret, Céline

AU - Morgan, Adam

AU - Muselli, Simone

AU - Nowell, Sarah

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DO - 10.1112/blms.12604

M3 - Article (Academic Journal)

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JF - Bulletin of the London Mathematical Society

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

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