Dual abelian varieties over a local field have equal volumes

Abstract: A top degree differential form $\omega$ on a smooth algebraic variety $X$ over a local field $K$ gives rise to a (real valued) measure on $X(K)$. The Serre duality yields a natural isomorphism between the vector spaces of global top degree forms on an abelian variety and the dual abelian variety. I will prove that the corresponding volumes are equal.

algebraic geometrynumber theory

Audience: researchers in the topic

( video )

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MIT number theory seminar

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