Arithmetic Properties of the Frobenius Traces Defined by a Rational Abelian Variety (with two appendices by J-P. Serre)
Arithmetic Properties of the Frobenius Traces Defined by a Rational Abelian Variety (with two appendices by J-P. Serre)
Let |$A$| be an abelian variety over |$\mathbb Q$| of dimension |$g$| such that the image of its associated absolute Galois representation |$\rho_A$| is open in |$\operatorname{GSp}_{2g}(\hat{ \mathbb Z})$|. We investigate the arithmetic of the traces |$a_{1, p}$| of the Frobenius at |$p$| in |$\operatorname{Gal}(\overline{\mathbb Q}/\mathbb Q)$| under |$\rho_A$|. In …