Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 53, Number 1 (2001), 175-235.
Euler characteristics and elliptic curves II
This paper describes a generalisation of the methods of Iwasawa Theory to the field obtained by adjoining the field of definition of all the -power torsion points on an elliptic curve, , to a number field, . Everything considered is essentially well-known in the case has complex multiplication, thus it is assumed throughout that has no complex multiplication. Let denote the Galois group of over . Then the main focus of this paper is on the study of the -cohomology of the Selmer group of over , and the calculation of its Euler characteristic, where possible. The paper also describes proposed natural analogues to this situation of the classical Iwasawa -invariant and the condition of having -invariant equal to 0.
The final section illustrates the general theory by a detailed discussion of the three elliptic curves of conductor 11, at the prime .
J. Math. Soc. Japan, Volume 53, Number 1 (2001), 175-235.
First available in Project Euclid: 9 June 2008
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COATES, John; HOWSON, Susan. Euler characteristics and elliptic curves II. J. Math. Soc. Japan 53 (2001), no. 1, 175--235. doi:10.2969/jmsj/05310175. https://projecteuclid.org/euclid.jmsj/1213023976