论文标题
$ \ mathrm {gl} _2 $ -Type在非常见的素数的Abelian Abelian品种的反风速iwasawa理论
Anticyclotomic Iwasawa theory of abelian varieties of $\mathrm{GL}_2$-type at non-ordinary primes
论文作者
论文摘要
令$ p \ ge 5 $为质数，$ e/\ mathbb {q} $是椭圆曲线，$ p $ p $ supersingular降低和$ k $一个想象的二次二次字段，以使$ e $ y $ k $的根号为$ k $是$+1 $。当$ p $以$ k $分配为$ k $时，达尔蒙（Darmon）和伊奥维塔（Iovita）提出了$ e $ $ e $的加号和负iwasawa的主要猜想。我们将它们的结果推广到两个新设置： 1。假设$ p $在$ k $中分配，但如果不假定$ a_p（e）= 0 $，我们研究了sprung-type iwasawa的主要猜想，用于$ \ mathrm {gl} _2 _2 $ -type的Abelian品种，并且证明是Anogous的包含。 2。我们制定，依靠Kobayashi和OTA的最新作者的最新作品，当$ k $中的$ p $时，椭圆曲线的iwasawa Main Main Main猜想，并证明是类似的包含。
Let $p\ge 5$ be a prime number, $E/\mathbb{Q}$ an elliptic curve with good supersingular reduction at $p$ and $K$ an imaginary quadratic field such that the root number of $E$ over $K$ is $+1$. When $p$ is split in $K$, Darmon and Iovita formulated the plus and minus Iwasawa main conjectures for $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$, and proved one-sided inclusion: an upper bound for plus and minus Selmer groups in terms of the associated $p$-adic $L$-functions. We generalize their results to two new settings: 1. Under the assumption that $p$ is split in $K$ but without assuming $a_p(E)=0$, we study Sprung-type Iwasawa main conjectures for abelian varieties of $\mathrm{GL}_2$-type, and prove an analogous inclusion. 2. We formulate, relying on the recent work of the first named author with Kobayashi and Ota, plus and minus Iwasawa main conjectures for elliptic curves when $p$ is inert in $K$, and prove an analogous inclusion.
