Curves and Jacobians
Let C be a curve of genus g ∈ N.
The Jacobian J of C is an Abelian variety of dimension g.
Abelian: group law on J, similarly to elliptic curves.
However, typically the equations of J are really horrible!
We want to compute in J by just looking at C.
NB Jacobian of a curve = Picard group of the curve ≈ class
group of a number field.
This is possible thanks to Makdisi’s algorithms.
Nicolas Mascot p-adic computation of Galois representations