2020/07/03 by Best, Alex J., Betts, L. Alexander, Bisatt, Matthew +8 · 2 citations
#11G20 (11G10 #14D10 #14G20 #14H45 #14Q05) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2007.01749
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.