What question did this study set out to answer?

The aim is to explore the p-divisibility of the Albanese kernel for products of curves over p-adic fields.

April 1, 2026Open Access

Bounds for the K-Groups Associated to Abelian Varieties Over a p-adic Field

Key Points

The aim is to explore the p-divisibility of the Albanese kernel for products of curves over p-adic fields.
Analyzed the structure of the Albanese map for products of curves
Investigated conditions under which Jacobian varieties have good ordinary reduction
Studied the effects of ramification on p-divisibility of algebraic structures
Confirmed that the Albanese kernel remains p-divisible when Jacobian varieties have good ordinary reduction
Established that this p-divisibility holds even if the base field has small ramification

Abstract

For a product of curves X = C1 × … ×Cn over a p-adic field k, in 2 we proposed a conjecture that the kernel of the Albanese map for X is p-divisible when the base field is absolutely unramified and proved this under some assumptions. In this note, we report that when the Jacobian varieties of such curves C1, …, Cn all have good ordinary reduction, the Albanese kernel for the product X = C1 × … × Cn is still p-divisible even if the base field is not unramified but its ramification is small enough.

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Toshiro Hiranouchi

Hiroshima University

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Bounds for the K-Groups Associated to Abelian Varieties Over a p-adic Field

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Abstract

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