What question did this study set out to answer?

This research aims to understand the kernel of the Albanese map for elliptic curves in p-adic fields.

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April 1, 2026Open Access

Elliptic Curves Over A p-adic Field With Fake Ordinary Good Reduction

Key Points

This research aims to understand the kernel of the Albanese map for elliptic curves in p-adic fields.
Analyzed the kernel structure for a product of elliptic curves.
Applied theoretical frameworks relevant to p-adic fields.
Examined the effect of field ramification on kernel properties.
Proved that the kernel becomes p-divisible under small ramification conditions.
Identified relationships between ramification and kernel attributes.

Abstract

We investigate the structure of the kernel of the Albanese map for a product of curves over a p-adic field. Specifically, we prove that the kernel becomes p-divisible when the ramification of the base field is sufficiently small.

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Cite This Study

Toshiro Hiranouchi (Sun,) studied this question.

synapsesocial.com/papers/69cd7b275652765b073a8e70 https://doi.org/https://doi.org/10.18997/0002000379