Torsion of algebraic groups and iterate extensions associated with Lubin–Tate formal groups

Abstract

We show finiteness results on torsion points of commutative algebraic groups over a $p$-adic field $K$ with values in various algebraic extensions $L/K$ of infinite degree. We mainly study the following cases: (1) $L$ is an abelian extension which is a splitting field of a crystalline character (such as a Lubin–Tate extension). (2) $L$ is a certain iterate extension of $K$ associated with points on Lubin–Tate formal groups.