5 papers · 1 filter
Kummer-faithful fields with finitely generated absolute Galois group
Takuya Asayama
This paper studies the structure of the Mordell--Weil groups of semiabelian varieties over algebraic extensions of number fields whose absolute Galois group is finitely generated,…
Mordell--Weil groups over large algebraic extensions of fields of characteristic zero
Takuya Asayama, Yuichiro Taguchi
We study the structure of the Mordell--Weil groups of semiabelian varieties over large algebraic extensions of a finitely generated field of characteristic zero. We consider two ty…
Kummer-faithfulness for function fields
Takuya Asayama
A perfect field is said to be Kummer-faithful if the Mordell-Weil group of every semi-abelian variety over every finite extension of has no nonzero divisible element. The c…
Ramification of Tate modules for rank Drinfeld modules
Takuya Asayama, Maozhou Huang
In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modul…
Torsion points of Drinfeld modules over large algebraic extensions of finitely generated function fields
Takuya Asayama
Geyer and Jarden proved several results for torsion points of elliptic curves defined over the fixed field by finitely many elements in the absolute Galois group of a finitely gene…