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arXiv · 1509.01316

On Tate-Shafarevich groups of 1-motives over Galois extensions

Cristian D. Gonzalez-Aviles
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Abstract

Let K/F be a finite Galois extension of global fields with Galois group G and let M be a 1-motive over F. We discuss the kernel and cokernel of the restriction map Sha^{i}(F,M) --> Sha^{i}(K,M)^{G} for i=1 and 2, independently of any finiteness hypotheses. We show that these groups are finite and obtain, in particular, formulas for the corresponding quotient of group orders.

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Cristian D. Gonzalez-Aviles. 2016-01-18. On Tate-Shafarevich groups of 1-motives over Galois extensions. https://arxiv.org/abs/1509.01316

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