| Kiran Kedlaya |  |
 |
Date de l'exposé : 6 septembre 2013
Counting points on hyperelliptic curves in average polynomial time(after Harvey & Sutherland)
We describe an algorithm of Harvey, improved and implemented by Harvey and Sutherland, which given a hyperelliptic curve of genus g over Q computes its zeta function over F_p for all p <= N in such a way that the average time per prime is polynomial in g and log(N). The method is based on p-adic cohomology, specifically the algorithms of Kedlaya and Harvey; the key new observation is that one can set up the cohomology computation in a manner which is almost entirely independent of p, and thus reuse much of the computation.
