تقرير
Non-vanishing of Kolyvagin systems and Iwasawa theory
| العنوان: | Non-vanishing of Kolyvagin systems and Iwasawa theory |
|---|---|
| المؤلفون: | Burungale, Ashay, Castella, Francesc, Grossi, Giada, Skinner, Christopher |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | Let $E/\mathbb{Q}$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for the $p$-adic Tate module of $E$ derived from Heegner points on $E$ over ring class fields of an imaginary quadratic field $K$ is non-trivial. In this paper we prove Kolyvagin's conjecture in the cases where $p$ is a prime of good ordinary reduction for $E$ that splits in $K$ and a $p$-adic anticyclotomic Iwasawa Main Conjecture for $E/K$ holds. In particular, our results cover many cases where $p$ is an Eisenstein prime, complementing W. Zhang's progress towards the conjecture. Our methods also yield a proof of a refinement of Kolyvagin's conjecture expressing the divisibility index of the $p$-adic Heegner point Kolyvagin system in terms of the Tamagawa numbers of $E$, as conjectured by W. Zhang in 2014, as well as proofs of analogous results for the Kolyvagin systems obtained from the cyclotomic Euler system of Beilinson--Kato elements. Comment: 30 pages, comments are welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.09301 |
| رقم الأكسشن: | edsarx.2312.09301 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |