Tamagawa Torsors of an Abelian Variety
Abstract
For an abelian variety A over a number field K, we define the set of Tamagawa torsors of A at a prime v of K to be the set of principal homogeneous spaces of A over the completion Kv of K at v that are split by an unramified extension of Kv. In this paper, we study the arithmetic properties of the Tamagawa torsors.
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