On Refined Conjectures of Birch and Swinnerton-Dyer Type for Hasse-Weil-Artin $L$-Series

David Burns, King's College London, United Kingdom, and Daniel Macias Castillo, Universidad Autonoma de Madrid, Spain, and Instituto de Ciencias Matematicas, Madrid, Spain.

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