Title: Algebraic functional equation for Hida family
Abstract: We prove a functional equation for the characteristic ideal of the "big" Selmer group 𝒳(𝒯 ℱ /F cyc ) associated to an ordinary Hida family of elliptic modular forms over the cyclotomic ℤ p extension 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].
Publication Year: 2014
Publication Date: 2014-09-09
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 5
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