BSD Plan for 2007-04-16

1. This week: 
   * Galois Cohomology
   * Sha
   * Leading coefficient
   Next week -- p-adic analogues

2. Galois cohomology:
   Definition of H^n(G,A) for G a group and A an abelian group with
   a G-action. 
     * cocycles / coboundaries
     * also can construct via homological algebra as
           Ext^n_{Z[G]}(Z,A)   <--- get right!
     
3. The long exact sequence.

4. The inf-res sequence.

5. Examples:
     * kummer theory of fields
     * quadratic extensions of finite fields
     * descent on elliptic curves

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1. 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
New projects:
    a. Study computing L_p(E,T) mod p.
    b. Heegner points package in SAGE (they are coming up)