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

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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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