摘要翻译：
本文研究了Mazur和Coates分别提出的分圆Iwasawa理论和数域上阿贝尔变体的非交换Iwasawa理论的特征p函数域上阿贝尔变体的一个（p-adic）几何模拟。我们将证明在数域上得到的主要结果的一些类比，并研究在数域上没有发生的新现象。我们还提出了一个猜想，在数域上的情况下，它可以被认为是主猜想的对应体。\par这是自2005年以来发行的预印本，目前仍在提交过程中。在最近修改了以前版本中的一些技术错误，以及改进了论文的呈现方式后，我们决定通过存档更广泛地分发。
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英文标题：
《On the Selmer groups of abelian varieties over function fields of
  characteristic p>0》
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作者：
Tadashi Ochiai, Fabien Trihan
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/0705.2608