Duality of Selmer groups of an abelian variety over a number field

Saikat Biswas

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arXiv · 2502.04968

Duality of Selmer groups of an abelian variety over a number field

Saikat Biswas

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Abstract

Let $A$ be an abelian variety defined over a number field $K$ and let $A^{\vee}$ be the dual abelian variety. For an odd prime $p$, we consider two Selmer groups attached to $A[p]$ and relate the orders of these groups along with those of their corresponding duals to the order of the component groups of $A^{\vee}$ at primes $v$.

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Saikat Biswas. 2025-02-07. Duality of Selmer groups of an abelian variety over a number field. https://arxiv.org/abs/2502.04968

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