论文标题
盘子和希达 - 晶体蛋白P-ADIC L功能
Plectic points and Hida-Rankin p-adic L-functions
论文作者
论文摘要
Fornea和Gehrmann引入了Pletic点，这是当地Pointson椭圆曲线的某些张量产品，上面是任意数字字段$ f $。在等级$ r \ leq [f：\ mathbb {q}] $ - 情况下，它们猜想来自Mordell-Weil Group的基础的P-ADIC调节器，该基础定义了$ f $的二面级扩展。在本文中，我们定义了两个可变的反风速$ p $ ad-adig l功能，该功能附在了一个过度会议的模块化符号，这些模块化符号定义了$ f $和二次扩展$ k/f $。它们对体重空间的限制提供了hida-rankin $ p $ - 亚种功能。如果这样的家庭通过附着在模块化椭圆曲线$ e/f $的过度融合模块化符号，我们将获得$ p $ - 亚种的总质量固定公式，该公式计算出此类hida-rankin $ p $ p $ p $ ad的l-functions的较高衍生物。该结果概括了Bertolini和Darmon的结果，这是证明Darmon Points合理性的关键。
Plectic points were introduced by Fornea and Gehrmann as certain tensor products of local pointson elliptic curves over arbitrary number fields $F$. In rank $r\leq [F:\mathbb{Q}]$-situations, they conjecturally come from p-adic regulators of basis of the Mordell-Weil group defined over dihedral extensions of $F$. In this article we define two variable anticyclotomic $p$-adic L-functions attached to a family of overconvergent modular symbols defined over $F$ and a quadratic extension $K/F$. Their restriction to the weight space provide Hida-Rankin $p$-adic L-functions. If such a family passes through an overconvergent modular symbol attached to a modular elliptic curve $E/F$, we obtain a $p$-adic Gross-Zagier formula that computes higher derivatives of such Hida-Rankin $p$-adic L-functions in terms of plectic points. This result generalizes that of Bertolini and Darmon, which has been key to demonstrating the rationality of Darmon points.
