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On Tate–Shafarevich groups of 1-motives

Volume 177 / 2017

Cristian D. González-Avilés 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 $\varGamma$.

Authors

  • Cristian D. González-AvilésDepartamento de Matemáticas
    Universidad de La Serena
    Cisternas 1200
    La Serena 1700000, Chile
    e-mail

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