no. 1
Jacobians in isogeny classes of abelian surfaces over finite fields
[Jacobiennes dans les classes d’isogénie des surfaces abéliennes sur les corps finis]
Howe, Everett W.1 ; Nart, Enric2 ; Ritzenthaler, Christophe3
1 Center for Communications Research 4320 Westerra Court San Diego, CA 92121-1967 (USA)
2 Universitat Autònoma de Barcelona Departament de Matemàtiques Edifici C 08193 Bellaterra, Barcelona (Spain)
3 Institut de Mathématiques de Luminy UMR 6206 du CNRS Luminy, Case 907 13288 Marseille (France)
Annales de l'Institut Fourier, Tome 59 (2009) no. 1, pp. 239-289.

Nous donnons une réponse complète à la question de savoir quels sont les polynômes caractéristiques du Frobenius des courbes de genre 2 sur les corps finis.

We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus-2 curves over finite fields.

DOI : 10.5802/aif.2430
Classification : 11G20, 14G10, 14G15
Keywords: Curve, Jacobian, abelian surface, zeta function, Weil polynomial, Weil number
Mot clés : courbe, Jacobienne, surface abélienne, fonction zêta, polynôme de Weil, nombre de Weil

Howe, Everett W. 1 ; Nart, Enric 2 ; Ritzenthaler, Christophe 3

1 Center for Communications Research 4320 Westerra Court San Diego, CA 92121-1967 (USA)
2 Universitat Autònoma de Barcelona Departament de Matemàtiques Edifici C 08193 Bellaterra, Barcelona (Spain)
3 Institut de Mathématiques de Luminy UMR 6206 du CNRS Luminy, Case 907 13288 Marseille (France) 
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Howe, Everett W.; Nart, Enric; Ritzenthaler, Christophe. Jacobians in isogeny classes of abelian surfaces over finite fields. Annales de l'Institut Fourier, Tome 59 (2009) no. 1, pp. 239-289. doi : 10.5802/aif.2430. https://aif.centre-mersenne.org/articles/10.5802/aif.2430/

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