# 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

Contents
Full-Text PDF