What question did this study set out to answer?

The research aims to explore the Albanese kernel structure related to the product of curves over a p-adic field.

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April 1, 2026Open Access

Albanese Kernel of the Product of Curves Over A p-adic Field

Key Points

The research aims to explore the Albanese kernel structure related to the product of curves over a p-adic field.
Investigated the image of the Kummer map for an abelian variety over a p-adic field.
Provided a proof differing from existing literature, notably by E. Gazaki.
Studied the assumptions under which the structure emerges.
Characterized the structure of the Albanese kernel for the product of curves.
Established that the new proof approach sheds additional light on previously known results.

Abstract

In this short note, we investigate the image of the Kummer map associated to an abelian variety over a p-adic field. As a byproduct, we give the structure of the Albanese kernel of the product of curves over a p-adic field under some assumptions. The result has already known by E. Gazaki 1, but the proof is completely different.

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Cite This Study

Toshiro Hiranouchi (Wed,) studied this question.

synapsesocial.com/papers/69cd7b345652765b073a9086 https://doi.org/https://doi.org/10.18997/00008063