Selmer Groups of Elliptic Curves with Complex Multiplication
Keyword(s):
AbstractSuppose K is an imaginary quadratic field and E is an elliptic curve over a number field F with complex multiplication by the ring of integers in K. Let p be a rational prime that splits as in K. Let Epn denote the pn-division points on E. Assume that F(Epn) is abelian over K for all n ≥ 0. This paper proves that the Pontrjagin dual of the -Selmer group of E over F(Ep∞) is a finitely generated free Λ-module, where Λ is the Iwasawa algebra of . It also gives a simple formula for the rank of the Pontrjagin dual as a Λ-module.
2015 ◽
Vol 11
(04)
◽
pp. 1233-1257
Keyword(s):
Keyword(s):
Keyword(s):
2011 ◽
Vol 151
(2)
◽
pp. 229-243
◽
Keyword(s):
Keyword(s):
2014 ◽
Vol 66
(4)
◽
pp. 826-843
◽
Keyword(s):
1996 ◽
Vol 54
(2)
◽
pp. 267-274
Keyword(s):