Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures
Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures
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超奇异素数椭圆曲线的岩泽理论：一对主要猜想
DOI：
10.1016/j.jnt.2011.11.003
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发表时间：
2009
影响因子：
0.7
通讯作者：
Florian Sprung
中科院分区：
文献类型：
--
作者：
Florian Sprung
正文：我们将小林的岩泽理论的公式推广到包括ap = 0的情况，其中ap是Frobenius的迹。为了做到这一点，我们代数地构造了p-adic L-函数Lp和Lp，它们具有经典Pollack p-adic L-函数的良好增长性质，当ap=0且p为奇数时，它们实际上完全匹配。然后我们推广了小林的方法，定义了两个塞尔默群Sel_n和Sel_n，并提出了一个主要猜想，说明这些塞尔默群的每个特征理想都是由我们的p进L-函数Lp_n和Lp_n生成的.然后，我们使用加藤的结果来证明整除性声明。视频：有关本文的视频摘要，请单击此处或访问http://www.youtube.com/watch? v=Y7gPQsBZo6s。
TEXT: We extend Kobayashiʼs formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case ap≠0, where apis the trace of Frobenius. To do this, we algebraically construct p-adic L-functions Lp♯and Lp♭with the good growth properties of the classical Pollack p-adic L-functions that in fact match them exactly when ap=0 and p is odd. We then generalize Kobayashiʼs methods to define two Selmer groups Sel♯and Sel♭and formulate a main conjecture, stating that each characteristic ideal of the duals of these Selmer groups is generated by our p-adic L-functions Lp♯and Lp♭. We then use results by Kato to prove a divisibility statement. VIDEO: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=Y7gPQsBZo6s.