Functional equation of characteristic elements of abelian varieties over function fields (ℓ ≠ p)

• Verfasst von: Pal, Aprameyo [VerfasserIn]
• Titel: Functional equation of characteristic elements of abelian varieties over function fields (ℓ ≠ p)
• Verf.angabe: Aprameyo Pal
• Jahr: 2014
• Jahr des Originals: 2013
• Umfang: 31 S.
• Fussnoten: Gesehen am 07.09.2020 ; First published: 2 December 2013
• Titel Quelle: Enthalten in: International journal of number theory
• Ort Quelle: Singapore [u.a.] : World Scientific, 2005
• Jahr Quelle: 2014
• Band/Heft Quelle: 10(2014), 03, Seite 705-735
• ISSN Quelle: 1793-0421
• DOI: doi:10.1142/S1793042113501194
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 172902663X

Abstract

In this paper we apply methods from the number field case of Perrin-Riou [20] and Zábrádi [32] in the function field setup. In ℤℓ- and GL2-cases (ℓ ≠ p), we prove algebraic functional equations of the Pontryagin dual of Selmer group which give further evidence of the main conjectures of Iwasawa theory. We also prove some parity conjectures in commutative and non-commutative cases. As a consequence, we also get results on the growth behavior of Selmer groups in commutative and non-commutative extension of function fields.