Jan Tuitman (Leuven)

07.05.2015 - W01 0-006 (Wechloy), 16 Uhr c.t.

Point counting on curves: the general case

Kedlaya's algorithm computes the zeta function of a hyperelliptic curve over a finite field using the theory of p-adic cohomology. We have recently developed and implemented a generalisation of this algorithm that works for (almost) any curve. First, we will outline the theory involved. Then we will describe our algorithm and illustrate the main ideas by giving some examples. Finally, if time permits, we will talk about applying the algorithm to the problem of Coleman integration, which is work in progress.