Jacobians and Galois representations
Let C be a curve of genus g over Q, let J be its Jacobian, and
let ` ∈ N.
Then J(Q)[`] ' (Z/`Z)2g
, and the points of J[`] are not
defined over Q in general
Galois representation
ρJ,` : Gal(Q/Q) −→ Aut(J[`]) ' GSp2g (Z/`Z).
Nicolas Mascot p-adic computation of Galois representations