On Tate-Shafarevich groups of 1-motives over Galois extensions
arXiv:1509.01316
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.
I withdraw this paper because the complicated formulas in it are practically useless. However, part of the material in it has been included in my next submission