Abstract
AbstractLet E/ℚ be an elliptic curve with good ordinary reduction at a prime p > 2. It has a welldefined Iwasawa μ-invariant μ(E)p which encodes part of the information about the growth of the Selmer group ) as Kn ranges over the subfields of the cyclotomic Zp-extension K∞/ℚ. Ralph Greenberg has conjectured that any such E is isogenous to a curve E′ with μ(E′)p = 0. In this paper we prove Greenberg's conjecture for infinitely many curves E with a rational p-torsion point, p = 3 or 5, no two of our examples having isomorphic p-torsion. The core of our strategy is a partial explicit evaluation of the global duality pairing for finite flat group schemes over rings of integers.
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