Algebraic functional equation for Hida family
Algebraic functional equation for Hida family
复制标题
Hida族代数函数方程
DOI：
10.1142/s1793042114500493
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Aprameyo
中科院分区：
文献类型：
--
作者：
Jha;Somnath; Pal;Aprameyo
证明了一般数域F的分圆扩张上的“大”塞尔默群塞尔默的特征理想的一个函数方程.𝒯𝒳对于一般数域，没有证明普通希达族的二元分圆Iwasawa主猜想，这可以被认为是Iwasawa主猜想有效性的一个证据.证明的中心思想是证明Perrin-Riou [Groupes de塞尔默et accouplements; cas particulier des courbes elliptiques，Doc. Math.2003（2003）725-760，Extra Volume：Kazuya Kato's fifty-birthday]，通过在对应于算术点的各个塞尔默群上构造广义配对，并利用Ochiai的适当专门化技术[Euler system for Galois deformations，Ann. Inst. Fourier（Grenoble）55（1）（2005）113-146]。
We prove a functional equation for the characteristic ideal of the "big" Selmer group 𝒳(𝒯ℱ/Fcyc) associated to an ordinary Hida family of elliptic modular forms over the cyclotomic ℤpextension of a general number field F, under the assumption that there is at least one arithmetic specialization whose Selmer group is torsion over its Iwasawa algebra. For a general number field, the two-variable cyclotomic Iwasawa main conjecture for ordinary Hida family is not proved and this can be thought of as an evidence to the validity of the Iwasawa main conjecture. The central idea of the proof is to prove a variant of the result of Perrin-Riou [Groupes de Selmer et accouplements; cas particulier des courbes elliptiques,Doc. Math.2003(2003) 725–760, Extra Volume: Kazuya Kato's fiftieth birthday] by constructing a generalized pairing on the individual Selmer groups corresponding to the arithmetic points and make use of the appropriate specialization techniques of Ochiai [Euler system for Galois deformations,Ann. Inst. Fourier (Grenoble)55(1) (2005) 113–146].