The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
1. Introduction
2. Selmer complexes
3. The refined Birch and Swinnerton-Dyer conjecture
4. Periods and Galois-Gauss sums
5. Local points on ordinary varieties
6. Classical Selmer complexes and refined BSD
7. Euler characteristics and Galois structures
8. Abelian congruence relations and module structures
9. Abelian congruence relations and height pairings
10. Height pairing comparisons
11. Modular symbols
12. Heegner points
A. Refined BSD and equivariant Tamagawa numbers
B. Poitou-Tate duality
C. Bockstein homomorphisms
David Burns, King's College London, United Kingdom, and Daniel Macias Castillo, Universidad Autonoma de Madrid, Spain, and Instituto de Ciencias Matematicas, Madrid, Spain.
