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 $K_v$ of $K$ at $v$ that are split by an unramified extension of $K_v$. In this paper, we study the arithmetic properties of the Tamagawa torsors.

References in corpus (1)

• Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field

Cited by in corpus (1)

• Groups of components of Néron models of Jacobians and Brauer groups