Iwasawa theory for elliptic curves at supersingular primes: A pair of main conjectures

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• 作者：Florian E. Ito Sprung ^{ian.sprung@gmail.com}
• 关键词：Elliptic curves ; Iwasawa theory ; Supersingular primes
• 刊名：Journal of Number Theory
• 出版年：2012
• 期刊代码：78_0022314x
• 类别：mt
• 出版时间：July, 2012
• 卷：132
• 期：7
• 页码：1483-1506
• 文件大小：315 K

摘要

Text

We extend Kobayashi始s formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case , where is the trace of Frobenius. To do this, we algebraically construct p-adic L-functions and with the good growth properties of the classical Pollack p-adic L-functions that in fact match them exactly when and p is odd. We then generalize Kobayashi始s methods to define two Selmer groups and 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 and . We then use results by Kato to prove a divisibility statement.

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