Mathematics – Number Theory
Scientific paper
1999-06-19
Mathematics
Number Theory
Abstract added in migration (taken from Greenberg's web site)
Scientific paper
10.1007/s002220000080
Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q. It is conjectured that Sel_E(Q_{oo}) is a cotorsion Lambda-module and that its characteristic ideal is related to the p-adic L-function associated to E. Under certain hypotheses we prove that the validity of these conjectures is preserved by congruences between the Fourier expansions of the associated modular forms.
Greenberg Ralph
Vatsal Vinayak
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