On the Selmer groups of abelian varieties over function fields of characteristic p>0

Abstract

In this paper, we study a (p-adic) geometric analogue for abelian varieties over a function field of characteristic p of the cyclotomic Iwasawa theory and the non-commutative Iwasawa theory for abelian varieties over a number field initiated by Mazur and Coates respectively. We will prove some analogue of the principal results obtained in the case over a number field and we study new phenomena which did not happen in the case of number field case. We propose also a conjecture which might be considered as a counterpart of the principal conjecture in the case over a number field. \par This is a preprint which is distributed since 2005 which is still in the process of submision. Following a recent modification of some technical mistakes in the previous version of the paper as well as an amelioration of the presentation of the paper, we decide wider distribution via the archive.

21 pages

References in corpus (1)

• The GL_2 main conjecture for elliptic curves without complex multiplication

Cited by in corpus (11)

• Selmer groups and class groups
• On the $\mu$-invariants of abelian varieties over function fields of positive characteristic
• On the Iwasawa Main conjecture of abelian varieties over function fields
• On a noncommutative Iwasawa main conjecture for varieties over finite fields
• Pontryagin duality for Iwasawa modules and abelian varieties
• Iwasawa theory of fine Selmer groups over global fields
• On $\mu$-invariants and isogenies for abelian varieties over function fields
• The Iwasawa main conjecture for semistable abelian varieties over function fields
• Finiteness and cofiniteness of fine Selmer groups over function fields
• Control Theorems for Abelian Varieties over Function Fields
• Non-commutative Iwasawa theory of abelian varieties over global function fields