Algebraic functional equation for Hida family
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 ℤp extension of a general number field F, under the assumption that there is at least one arithmetic speciali...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 March 2014
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| In: |
International journal of number theory
Year: 2014, Volume: 10, Issue: 7, Pages: 1649-1674 |
| ISSN: | 1793-0421 |
| DOI: | 10.1142/S1793042114500493 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S1793042114500493 Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/abs/10.1142/S1793042114500493 
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| Author Notes: | Somnath Jha, Aprameyo Pal |
| Summary: | 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 ℤp 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]. |
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| Item Description: | Gesehen am 08.04.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1793-0421 |
| DOI: | 10.1142/S1793042114500493 |