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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 March 2014
|
| 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 
|
| Author Notes: | Somnath Jha, Aprameyo Pal |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 175338057X | ||
| 003 | DE-627 | ||
| 005 | 20220819160554.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 210408s2014 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1142/S1793042114500493 |2 doi | |
| 035 | |a (DE-627)175338057X | ||
| 035 | |a (DE-599)KXP175338057X | ||
| 035 | |a (OCoLC)1341403906 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Jha, Somnath |e VerfasserIn |0 (DE-588)1231034890 |0 (DE-627)175338107X |4 aut | |
| 245 | 1 | 0 | |a Algebraic functional equation for Hida family |c Somnath Jha, Aprameyo Pal |
| 264 | 1 | |c 26 March 2014 | |
| 300 | |a 26 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 08.04.2021 | ||
| 520 | |a We prove a functional equation for the characteristic ideal of the "big" Selmer group (ℱ/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]. | ||
| 700 | 1 | |a Pal, Aprameyo |e VerfasserIn |0 (DE-588)1034706209 |0 (DE-627)746186169 |0 (DE-576)382338014 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t International journal of number theory |d Singapore [u.a.] : World Scientific, 2005 |g 10(2014), 7, Seite 1649-1674 |h Online-Ressource |w (DE-627)497607670 |w (DE-600)2200412-9 |w (DE-576)120281813 |x 1793-0421 |7 nnas |a Algebraic functional equation for Hida family |
| 773 | 1 | 8 | |g volume:10 |g year:2014 |g number:7 |g pages:1649-1674 |g extent:26 |a Algebraic functional equation for Hida family |
| 856 | 4 | 0 | |u https://doi.org/10.1142/S1793042114500493 |x Verlag |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 856 | 4 | 0 | |u https://www.worldscientific.com/doi/abs/10.1142/S1793042114500493 |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20210408 | ||
| 993 | |a Article | ||
| 994 | |a 2014 | ||
| 998 | |g 1034706209 |a Pal, Aprameyo |m 1034706209:Pal, Aprameyo |p 2 |y j | ||
| 999 | |a KXP-PPN175338057X |e 3903906387 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"recId":"175338057X","language":["eng"],"type":{"media":"Online-Ressource","bibl":"article-journal"},"note":["Gesehen am 08.04.2021"],"title":[{"title":"Algebraic functional equation for Hida family","title_sort":"Algebraic functional equation for Hida family"}],"person":[{"roleDisplay":"VerfasserIn","display":"Jha, Somnath","role":"aut","family":"Jha","given":"Somnath"},{"role":"aut","roleDisplay":"VerfasserIn","display":"Pal, Aprameyo","given":"Aprameyo","family":"Pal"}],"relHost":[{"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"dateIssuedDisp":"2005-","dateIssuedKey":"2005","publisher":"World Scientific","publisherPlace":"Singapore [u.a.]"}],"id":{"zdb":["2200412-9"],"eki":["497607670"],"issn":["1793-0421"]},"disp":"Algebraic functional equation for Hida familyInternational journal of number theory","note":["Gesehen am 20.10.22"],"type":{"bibl":"periodical","media":"Online-Ressource"},"language":["eng"],"recId":"497607670","pubHistory":["1.2005 -"],"part":{"text":"10(2014), 7, Seite 1649-1674","volume":"10","extent":"26","year":"2014","pages":"1649-1674","issue":"7"},"title":[{"title_sort":"International journal of number theory","subtitle":"(IJNT)","title":"International journal of number theory"}]}],"physDesc":[{"extent":"26 S."}],"id":{"eki":["175338057X"],"doi":["10.1142/S1793042114500493"]},"origin":[{"dateIssuedKey":"2014","dateIssuedDisp":"26 March 2014"}],"name":{"displayForm":["Somnath Jha, Aprameyo Pal"]}} | ||
| SRT | |a JHASOMNATHALGEBRAICF2620 | ||