Jacobians in isogeny classes of abelian surfaces over finite fields

Howe, Everett W.; Nart, Enric; Ritzenthaler, Christophe

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.

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

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