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한국고등과학원 세미나 



[GSNT] Nonexistence of nontrivial finite $Lambda$submodules of +/ Selmer groups 

Takahiro Kitajima (Keio University ) 
Let $E$ be an elliptic curve over $?mathbb Q$ which has supersingular reduction at some odd prime number $p$, $F$ a finite abelian number field and $F_{?infty}/F$ the cyclotomic $?mathbb Z_p$extension. Assume that $a_p=0$. Then Kobayashi defined the plus and the minus Selmer groups of $E$ over $F_{?infty}$ and proved that their Pontryagin duals are $?Lambda$torsion. It is a basic question whether the Pontryagin duals of the plus and the minus Selmer groups of $E$ over $F_{infty}$ have nontrivial finite $Lambda$submodules or not. In this talk, we present a result on the nonexistence of nontrivial ?nite $Lambda$submodules. Our result is a generalization of B.D. Kim's result in 2013. This is joint work with R. Otsuki. 







