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28 March 2024
 
  » arxiv » 2007.1749

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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 ;
Date 3 Jul 2020
AbstractA 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.
Source arXiv, 2007.1749
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