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arXiv · 2511.04186

Kummer-faithfulness over $p$-adic fields

Yoshiyasu Ozeki
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Abstract

The notion of a Kummer-faithful field, defined by Mochizuki, is expected as one of suitable base fields for anabelian geometry. In this paper, we study Kummer-faithfulness for algebraic extension fields of $p$-adic fields. We show that Kummer-faithfulness for such fields are deeply related with various finiteness properties on torsion points of (semi-)abelian varieties. For example, a Galois extension $K$ of a $p$-adic field is Kummer-faithful with finite residue field if and only if, for any finite extension $L$ of $K$ and any abelian variety over $L$,its $L$-rational torsion subgroup is finite. In addition, we study Kummer-faithfulness for Lubin-Tate extension fields.

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Yoshiyasu Ozeki. 2025-11-06. Kummer-faithfulness over $p$-adic fields. https://arxiv.org/abs/2511.04186

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