2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146224Let E be an elliptic curve defined over a finite field. Balasubramanian and Koblitz have proved that if the l-th roots of unity m_l is not contained in the ground field, then a field extension of the ground field contains m_l if and only if the l-torsion points of E are rational over the same field extension. We generalize this result to Jacobians of genus two curves with complex multiplication. In particular, we show that the Weil- and the Tate-pairing on such a Jacobian are non-degenerate over the same field extension of the ground field.The paper was presented at AGCT 11, november 2007Algebraic Geometry14H40 (Primary); 11G15, 14Q05, 94A60 (Secondary)text