  We 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.
