Selmer Groups over p-adic Lie Extensions I


Let EE be an elliptic curve defined over a number field FF. In this paper, we study the structure of the p∞p^\infty-Selmer group of EE over pp-adic Lie extensions F∞F_\infty of FF which are obtained by adjoining to FF the pp-division points of an abelian variety AA defined over FF. The main focus of the paper is the calculation of the \Gal(F_\infty/F)-Euler characteristic of the p∞p^\infty-Selmer group of EE. The final section illustrates the main theory with the example of an elliptic curve of conductor 294.Comment: 23 page

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    Last time updated on 01/04/2019