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 

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,P.R.China [2]School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第2期289-305,共17页数学学报（英文版）

基　　金：The second author is supported by National Natural Science Foundation of China(Grant Nos.11550110172 and 11771164)。

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 ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-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.

关 键 词：Algebraic functional equation mixed signed Selmer groups 

分 类 号：O175[理学—数学] O152[理学—基础数学]