On signed Mordell-Weil groups for abelian varieties

Abstract: In this short note, we work in the general framework of supersingular abelian varieties defined over $\mathbb{Q}$. Using Coleman maps constructed by Buuyukboduk--Lei, we define some new objects called ``the multi-signed Mordell-Weil groups" for supersingular abelian varieties, provide an explicit structure of the dual of these groups as an Iwasawa module and prove a control theorem. This recovers the case of elliptic curves over $\mathbb{Q}$ non-ordinary at the prime $p$ with $a_p=0$ studied by Antonio Lei.