探討橢圓曲線經扭變後之秩

Abstract

For an elliptic curve, we care about the Mordell-Weil group on it. Espically we care about the rank of this group. On the other hand, it is known that the F2-dimension of Selmer group of an elliptic curve is an finite upper bound of the rank of the Mordell-Weil group. In this thesis, we study the result of Mazur and Rubin. They view the Selmer group and the twisted Selmer group as contained in the same set. Analyzing the local Selmer group, which tells us when will them be the same or intersect to zero. By this we can see the relation between the dimension of Selmer group and that of twisted Selmer group. Then we know that under some conditions, elliptic curve have abitrary twisted Selmer rank. IV