Geodesic
Galois representations of superelliptic curves
Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 356-382

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DOI

A superelliptic curve over a discrete valuation ring $\mathscr{O}$ of residual characteristic p is a curve given by an equation $\mathscr{C}\;:\; y^n=\,f(x)$, with $\textrm{Disc}(\,f)\neq 0$. The purpose of this article is to describe the Galois representation attached to such a curve under the hypothesis that f(x) has all its roots in the fraction field of $\mathscr{O}$ and that $p \nmid n$. Our results are inspired on the algorithm given in Bouw and WewersGlasg (Math. J. 59(1) (2017), 77–108.) but our description is given in terms of a cluster picture as defined in Dokchitser et al. (Algebraic curves and their applications, Contemporary Mathematics, vol. 724 (American Mathematical Society, Providence, RI, 2019), 73–135.).
DOI : 10.1017/S0017089522000386
Mots-clés : Superelliptic Curves, Galois representations 
Pacetti, Ariel; Villanueva, Angel. Galois representations of superelliptic curves. Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 356-382. doi: 10.1017/S0017089522000386
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     title = {Galois representations of superelliptic curves},
     journal = {Glasgow mathematical journal},
     pages = {356--382},
     year = {2023},
     volume = {65},
     number = {2},
     doi = {10.1017/S0017089522000386},
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