Integral Iwasawa theory of galois representations for non-ordinary primes
Integral Iwasawa theory of galois representations for non-ordinary primes
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DOI：
10.1007/s00209-016-1765-z
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发表时间：
2015-11
影响因子：
0.8
通讯作者：
Kâzım Büyükboduk;Antonio Lei
中科院分区：
文献类型：
--
作者：
Kâzım Büyükboduk;Antonio Lei
在这篇论文中，我们研究了一个动机的Iwasawa理论，它的Hodge-Tate权值为0或1（因此在实践中，动机是与一个阿贝变相关的）在一个非普通素数上，在一个完全实数或CM数域的分环塔上。特别地，在一定的技术假设下，我们在局部Iwasawa上同调群上构造了spring -type Coleman映射，并利用它们定义了积分- adicl函数和（一个无条件地，另一个猜想地）cotorselmer群。这使我们能够根据这些物体重新制定Perrin-Riou的主要猜想，就像Kobayashi关于超奇异椭圆曲线的±-Iwasawa理论一样。借助于本文发展的coleman - adaptive Kolyvagin系统理论，我们从显式互易猜想中推导出Perrin-Riou主要猜想的部分内容。
In this paper, we study the Iwasawa theory of a motive whose Hodge–Tate weights are 0 or 1 (thence in practice, of a motive associated to an abelian variety) at a non-ordinary prime, over the cyclotomic tower of a number field that is either totally real or CM. In particular, under certain technical assumptions, we construct Sprung-type Coleman maps on the local Iwasawa cohomology groups and use them to define integralp-adicL-functions and (one unconditionally and other conjecturally) cotorsion Selmer groups. This allows us to reformulate Perrin–Riou’s main conjecture in terms of these objects, in the same fashion as Kobayashi’s ±-Iwasawa theory for supersingular elliptic curves. By the aid of the theory ofColeman-adapted Kolyvagin systemswe develop here, we deduce parts of Perrin–Riou’s main conjecture from an explicit reciprocity conjecture.