no. 2
Root number of the Jacobian of y 2 =x p +a
Bisatt, Matthew1
1 Fry Building University of Bristol Bristol, BS8 1UG, UK
Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 2, pp. 575-582.

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.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1217
Classification: 11G20, 11G40
Keywords: Root numbers, hyperelliptic curves
Bisatt, Matthew 1

1 Fry Building University of Bristol Bristol, BS8 1UG, UK 
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Bisatt, Matthew. Root number of the Jacobian of $y^2=x^p+a$. Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 2, pp. 575-582. doi : 10.5802/jtnb.1217. http://www.numdam.org/articles/10.5802/jtnb.1217/

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