On Tate–Shafarevich groups of 1-motives
Volume 177 / 2017
Acta Arithmetica 177 (2017), 75-89
MSC: Primary 11G35; Secondary 14G25.
DOI: 10.4064/aa8489-8-2016
Published online: 9 November 2016
Abstract
We establish the finiteness of the kernel and cokernel of the restriction map ${\rm res}^{i}\colon Ш^{i}(F,M)\to Ш^{i}(K,M)^{\varGamma}$ for $i=1$ and $2$, where $M$ is a (Deligne) $1$-motive over a global field $F$, and $K/ F$ is a finite Galois extension of global fields with Galois group $\varGamma$.
