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.