Abstract
We reduce the chromatic Iwasawa main conjecture for elliptic curves to the conjectured existence of certain Beilinson–Flach classes in the supersingular case. This generalizes the method of Wan in which ap=0 was assumed; the main innovation of this paper consists in the new 2-dimensional technique to overcome this condition. We also derive the 3-part of the leading term formula in the Birch and Swinnerton-Dyer conjecture for analytic rank 0 or 1 from the main conjecture. Another consequence is that among those elliptic curves with a prescribed number of solutions modulo any fixed prime, infinitely many would satisfy the full Birch and Swinnerton-Dyer conjecture.
Original language | English (US) |
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Article number | 109741 |
Journal | Advances in Mathematics |
Volume | 449 |
DOIs | |
State | Published - Jul 2024 |
Keywords
- Birch and Swinnerton-Dyer
- Elliptic curve
- Iwasawa theory
ASJC Scopus subject areas
- General Mathematics