Journal of the Ramanujan Mathematical Society

Volume 30, Issue 1, March 2015 pp. 67–81.

Tamagawa torsors of an Abelian variety

Authors: Saikat Biswas
Author institution:School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287.

Summary: For an abelian variety A/K 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 some of the arithmetic properties of the Tamagawa torsors. We also give, following Mazur's theory of visibility, conditions under which non-trivial elements of the Tamagawa torsors of A may be interpreted as rational points on another abelian variety B.

Keywords: Iwasawa cohomology groups, fine Selmer groups, S-admissible p-adic Lie extensions, Euler characteristics

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