Root number of the Jacobian of y 2 =x p +a
Matthew Bisatt1
1 Fry Building University of Bristol Bristol, BS8 1UG, UK
Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 2, pp. 575-582.

Soit C/ℚ une courbe hyperelliptique donnée par un modèle affine de la forme y 2 =x p +a. Nous déterminons le signe de la Jacobienne de C, en particulier nous nous concentrons sur le signe local en p, où C est sauvagement ramifiée.

Let C/ℚ be a hyperelliptic curve with an affine model of the form y 2 =x p +a. We explicitly determine the root number of the Jacobian of C, with particular focus on the local root number at p where C has wild ramification.

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DOI : 10.5802/jtnb.1217
Classification : 11G20, 11G40
Mots clés : Root numbers, hyperelliptic curves
Matthew Bisatt 1

1 Fry Building University of Bristol Bristol, BS8 1UG, UK
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Journal de th\'eorie des nombres de Bordeaux},
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Matthew Bisatt. Root number of the Jacobian of $y^2=x^p+a$. Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 2, pp. 575-582. doi : 10.5802/jtnb.1217. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1217/

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