Jacobians and Galois representations
With Riemann-Roch spaces, we can construct a Makdisi
model of the Jacobian J of C.
At the moment, only implemented for models of J over Zq/pe
,
where q = pd
with p a prime of good reduction, Zq is the ring
of integers of the unramified extension of Qp of degree d, and
e ∈ N is arbitrary.
But no difficulty for models of J over number fields.
p-adic models of J can be used to compute Galois
representations occurring in the torsion of J.
C=CrvInit(x^5 + y^5 - 6*x^3 + 6*x^2 + x*y - 3*y^2);
CrvPrint(C)
CrvPicTorsGalRep(C,2,13,700)
Nicolas Mascot Algebraic curves