Représentations Galoisiennes Associées Aux Courbes Hyperelliptiques Lisses

huyghe, christine; wach, nathalie;

In 2003, Kedlaya gave an algorithm to compute the zeta function associated to a hyperelliptic curve over a finite field, by computing the rigid cohomology of the curve. Edixhoven remarked that it
is actually possible to compute the crystalline cohomology of the curve, which is a lattice in the rigid cohomology. Following a method of Wach, we explain how to use this lattice to compute the (ϕ, )-module associated to an hyperelliptic curve.