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

Toshiro Hiranouchi

doi:10.18997/0002000379

March 31, 2024Open Access

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

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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.

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Implication

Investigation reveals p-divisibility of kernel in elliptic curves, indicating impact of ramification.

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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Toshiro Hiranouchi (2024) studied this question.

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

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

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Abstract

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

Key Points

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Implication

Abstract

Discussion

Cite This Study

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