论文标题
关于艾森斯坦素数的反合气体硫泽理论理论
On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes
论文作者
论文摘要
令$ e/\ mathbb {q} $为椭圆曲线，而$ p $ a Prime $ e $的减少良好，并假设$ e $承认有理$ p $ - 发育。在本文中，我们研究了$ e $的反风速浮游理论，这是一个虚构的二次领域，其中$ p $ splits（我们遵循格林伯格 - 瓦塔萨尔的方法，我们与反合气体伊瓦苏瓦理论有关。 As a result of our study, we obtain a proof, under mild hypotheses, of Perrin-Riou's Heegner point main conjecture, as well as a $p$-converse to the theorem of Gross--Zagier and Kolyvagin and the $p$-part of the Birch--Swinnerton-Dyer formula in analytic rank $1$ for Eisenstein primes $p$.
Let $E/\mathbb{Q}$ be an elliptic curve, and $p$ a prime where $E$ has good reduction, and assume that $E$ admits a rational $p$-isogeny. In this paper, we study the anticyclotomic Iwasawa theory of $E$ over an imaginary quadratic field in which $p$ splits, which we relate to the anticyclotomic Iwasawa theory of characters following the method of Greenberg--Vatsal. As a result of our study, we obtain a proof, under mild hypotheses, of Perrin-Riou's Heegner point main conjecture, as well as a $p$-converse to the theorem of Gross--Zagier and Kolyvagin and the $p$-part of the Birch--Swinnerton-Dyer formula in analytic rank $1$ for Eisenstein primes $p$.
