On the Algebraic Functional Equation of the Eigenspaces of Mixed Signed Selmer Groups of Elliptic Curves with Good Reduction at Primes above p

• 作者: Suman AHMED Meng Fai LIM
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 289-305
• 页数: 17页
• 语种: 英文

摘要

Let p be an odd prime number, and let E be an elliptic curve defined over a number field which has good reduction at every prime above p. Under suitable assumptions, we prove that the η-eigenspace and the (η)-eigenspace of mixed signed Selmer group of the elliptic curve are pseudo-isomorphic. As a corollary, we show that the η-eigenspace is trivial if and only if the (η)-eigenspace is trivial. Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a"reflected"eigenspace.