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

David Burns, Daniel Macias Castillo (Autoren)

Buch | Softcover

156 Seiten

2024
American Mathematical Society (Verlag)
978-1-4704-6966-5 (ISBN)

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Publishing extended research in pure and applied mathematics, the series brings together groups of related papers into cohesive volumes. Guided by an esteemed Editorial Committee from the AMS Transactions, each paper endures rigorous peer review to ensure deep scholarly insight and precision.

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.

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

Erscheinungsdatum	22.08.2024
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	1-4704-6966-9 / 1470469669
ISBN-13	978-1-4704-6966-5 / 9781470469665
Zustand	Neuware