论文标题
Selmer组的结构和椭圆曲线的伊瓦川主要猜想
The structure of Selmer groups and the Iwasawa main conjecture for elliptic curves
论文作者
论文摘要
我们揭示了（比弱）的新的且精致的应用（较弱的陈述），用于椭圆形曲线的伊瓦岛主要猜想，以与任意等级的椭圆形曲线组的结构。对于一大批椭圆曲线，我们获得以下算术后果。 1。Kato的Kolyvagin系统是非平凡的。它是kolyvagin猜想的循环类似物。 2。完全根据某些模块化符号确定了椭圆曲线的Selmer组的结构。它是桦木和Swinnerton-Dyer猜想的结构改进。 3。等级零$ p $ - converse，$ p $ - parity的猜想以及椭圆曲线等级的新上限。 4。确认了Kurihara对Mod $ P $ Selmer组的半本地描述的猜想。 5。讨论了$ p $ - adic桦木和Swinnerton-dyer猜想的申请。
We reveal a new and refined application of (a weaker statement than) the Iwasawa main conjecture for elliptic curves to the structure of Selmer groups of elliptic curves of arbitrary rank. For a large class of elliptic curves, we obtain the following arithmetic consequences. 1. Kato's Kolyvagin systems is non-trivial. It is the cyclotomic analogue of the Kolyvagin conjecture. 2. The structure of Selmer groups of elliptic curves over the rationals is completely determined in terms of certain modular symbols. It is a structural refinement of Birch and Swinnerton-Dyer conjecture. 3. The rank zero $p$-converse, the $p$-parity conjecture, and a new upper bound of the ranks of elliptic curves are obtained. 4. The conjecture of Kurihara on the semi-local description of mod $p$ Selmer groups is confirmed. 5. An application of the $p$-adic Birch and Swinnerton-Dyer conjecture to the structure of Iwasawa modules is discussed.
