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On the indivisibility of derived Kato’s Euler systems and the main conjecture for modular forms
Selecta Mathematica ( IF 1.2 ) Pub Date : 2020-04-16 , DOI: 10.1007/s00029-020-00554-w
Chan-Ho Kim , Myoungil Kim , Hae-Sang Sun

We provide a simple and efficient numerical criterion to verify the Iwasawa main conjecture and the indivisibility of derived Kato’s Euler systems for modular forms of weight two at any good prime under mild assumptions. In the ordinary case, the criterion works for all members of a Hida family once and for all. The key ingredient is the explicit computation of the integral image of the derived Kato’s Euler systems under the dual exponential map. We provide explicit new examples at the end. This work does not appeal to the Eisenstein congruence method at all.

中文翻译:

关于派生的加藤的欧拉系统的不可分性和模块化形式的主要猜想

我们提供了一个简单而有效的数值准则,以验证岩泽主猜想以及在轻度假设下,在任何良好的素数下,重量为二的模块形式的加藤Euler系统对于模数形式的不可分性。在通常情况下,该准则一劳永逸地适用于飞ida家族的所有成员。关键因素是在双指数映射下显式计算派生的Kato's Euler系统的积分图像。最后,我们提供了明确的新示例。这项工作完全不符合爱森斯坦全等方法。
更新日期:2020-04-16
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