This article is cited in 2 scientific papers (total in 2 papers)
On the Galois cohomology of elliptic curves defined over a local field
O. N. Vvedenskii
In this article we calculate the group of principal homogeneous spaces over elliptic curves defined over a complete discretely normed field with algebraically closed residue field of characteristic $p>3$ and belonging to types $(c 4)$, $(c 5)$ in the classification of A. Neron. The result of our calculations refutes Neron's earlier statement that the group of principal homogeneous spaces over curves of type $(c)$ is trivial. Moreover the calculation of the fundamental group of the proalgebraic group of the points on these curves that are rational over the ground field supports (in this case) the conjecture of I. R. Shafarevich concerning the duality of the group of principal homogeneous spaces and the character group of the fundamental group.
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Mathematics of the USSR-Sbornik, 1970, 12:3, 477–488
MSC: 11S25, 12G05, 11E72, 12J05, 20K30, 11G07
O. N. Vvedenskii, “On the Galois cohomology of elliptic curves defined over a local field”, Mat. Sb. (N.S.), 83(125):3(11) (1970), 474–484; Math. USSR-Sb., 12:3 (1970), 477–488
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\paper On~the Galois cohomology of elliptic curves defined over a~local field
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
O. N. Vvedenskii, “On quasi-local “class fields” of elliptic curves. I”, Math. USSR-Izv., 10:5 (1976), 913–936
Qing Liu, Dino Lorenzini, Michel Raynaud, “Néron models, Lie algebras, and reduction of curves of genus one”, Invent math, 157:3 (2004), 455
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