Description
Kedlaya described an algorithm for computing the zeta function of a hyperelliptic curve in characteristic p > 2 using the theory of Monsky-Washnitzer cohomology. Joint work with Jan Denef has resulted in 2 extensions of Kedlaya's original algorithm: the first extension can be used to compute the zeta function of a hyperelliptic curve in characteristic 2 and the second leads to a rather general method which works for any C_ab curve in any small characteristic. Furthermore, results obtained with an implemtation of both algorithms will be presented.