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

Published online by Cambridge University Press:  01 January 2009

TADASHI OCHIAI  and
FABIEN TRIHAN
TADASHI OCHIAI
Affiliation:
Department of Mathematics, Osaka University, 1-1, Machikaneyama Toyonaka, Osaka 560-0043Japan e-mail: [email protected]
FABIEN TRIHAN
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom. e-mail: [email protected]
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Abstract

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 also propose a conjecture (Conjecture 1.6) which might be considered as a counterpart of the principal conjecture in the case over a number field.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 23 - 43
Copyright
Copyright © Cambridge Philosophical Society 2008

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