查看文章

Let be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group does not vanish, and investigate the analogous question for when . We include an application to the verification of certain cases of the Birch and Swinnerton-Dyer conjecture, and another application to the Grunwald–Wang problem for elliptic curves.