The generalized Cassels-Tate dual exact sequence for 1-motives

TL;DR

This paper extends the Cassels-Tate dual exact sequence to 1-motives over global fields, broadening the scope from abelian varieties to more general 1-motives, and provides a unified duality framework.

Contribution

It introduces a generalized dual exact sequence for 1-motives, expanding the classical results from abelian varieties to a wider class of motives.

Findings

Established a dual exact sequence for 1-motives over global fields

Extended previous theorems from abelian varieties to 1-motives

Provides a unified duality framework for 1-motives

Abstract

We establish a generalized Cassels-Tate dual exact sequence for 1-motives over global fields. We thereby extend the main theorem of [4] from abelian varieties to arbitrary 1-motives.