2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63243We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over F_q with the given characteristic polynomial splits over F_{q^2} as a product of polarized elliptic curves.LaTeX, 13 pagesNumber TheoryAlgebraic Geometry11G20 (Primary); 11G10, 11R65, 14G15, 14H25 (Secondary)text