Selmer Groups over p-adic Lie Extensions I

Details Selmer Groups over p-adic Lie Extensions I Selmer Groups over p-adic Lie Extensions I

2004-04-09

arxiv.org/abs/math/0404203v1

J. London Math. Soc. 70(3), 2004, pp. 586--608

Mathematics

Number Theory

23 pages

Scientific paper

10.1112/S002461070400568X

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

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