  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 first explain how to use this
lattice to compute the $(\varphi,\Gamma)$-module associated to an hyperelliptic
curve. We also explain an alternative way to get the $(\varphi,\Gamma)$-module
mod $p$ that relies on the Deligne-Illusie morphism.
