BSD Plan for 2007-04-13

0. Talk about plan for rest of the course. 

1. Quickly write defn of P_n on board again.

2. Write out proof that P_n(zeta_r - 1) = int chi_r dmu

3. Cor: w_n(T) = (1+T)^(p^n) - 1 divides P_{n+1}(T) - P_n(T).

4. Then do lemma 1.23

5. Deduce the bound (prop 1.24).

6. Talk about projects:
 a. Robert B -- 2-descent
 b. Dustin M -- ap lists
 c. Robert M -- congruence graph
 d. Koopa K -- what we just did; finiteness of Sha's
 e. Ralph G -- What if ord_p(Reg) > 0?
New projects:
    a. Study computing L_p(E,T) mod p.
    b. Heegner points package in SAGE (they are coming up)