Computing torsion points on curves

Let X be a curve of, genus g greater than or equal to 2 over a field k of c haracteristic zero. Let X hooked right arrow A be an Albanese map associate d to a point P-0 on X. The Manin-Mumford conjecture, first proved by Raynau d, asserts that the set T of points in X((k) over bar) mapping to torsion p oints on A is finite. Using a p-adic approach, we develop an algorithm to c ompute T, and implement it in the case where k = Q, g = 2, and P-0 is a Wei erstrass point. Improved bounds on #T are also proved: for instance, in the context of the previous sentence, if in addition X has good reduction at a prime p greater than or equal to5, then #T 2p(3) + 2p(2) + 2p + 8.