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

2021/05/24 by Ozeki, Yoshiyasu · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2105.11049

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 Lubin-Tate formal groups, which is familiar with Kummer theory.

Cited by

• Kummer-faithfulness over p-adic fields
• Torsion of rank-two A-motives values in odd characteristic cyclotomic towers

Related

• Torsion of abelian varieties and Lubin-Tate extensions
• Torsion points of abelian varieties with values in infinite extensions over a p-adic field
• Iterated extensions and relative Lubin-Tate groups
• Torsion bounds for a fixed abelian variety and varying number field
• Constructing 2-dimensional Lubin-Tate formal groups over ℤ_p (I)