论文标题
反风速伊瓦沙理论中的Kolyvagin的猜想和修补的Euler系统
Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory
论文作者
论文摘要
令$ e/\ mathbb {q} $为椭圆曲线，让$ k $为虚构的二次字段。根据某个赫纳（Heegner）假设，Kolyvagin使用$ k $ -cm积分为$ e $构建了共同体课程，并猜想他们并没有消失。他以这种猜想为条件，使用他的班级系统描述了$ e $的Selmer等级。我们扩展了Wei Zhang的工作，以考虑模块化表格的一致性Modulo大国的概念，从而证明了Kolyvagin的猜想的新案例。此外，我们证明了一个类似的结果，并在互补的“确定”情况下（使用某些修改后的$ l $ - 价值而不是CM点）给出了Selmer等级的描述。还使用类似的方法来改善Perrin-Riou的Heegner Point主要猜想的已知结果。结果的结果之一是一个新的匡威定理，当残留表示为二面图像时，$ p $ -selmer等级意味着分析等级。
Let $E/\mathbb{Q}$ be an elliptic curve and let $K$ be an imaginary quadratic field. Under a certain Heegner hypothesis, Kolyvagin constructed cohomology classes for $E$ using $K$-CM points and conjectured they did not all vanish. Conditional on this conjecture, he described the Selmer rank of $E$ using his system of classes. We extend work of Wei Zhang to prove new cases of Kolyvagin's conjecture by considering congruences of modular forms modulo large powers of $p $. Additionally, we prove an analogous result, and give a description of the Selmer rank, in a complementary "definite" case (using certain modified $L$-values rather than CM points). Similar methods are also used to improve known results on the Heegner point main conjecture of Perrin-Riou. One consequence of our results is a new converse theorem, that $p$-Selmer rank one implies analytic rank one, when the residual representation has dihedral image.
