# Journal of the Ramanujan Mathematical Society

Volume 33, Issue 2, June 2018 pp. 205–217.

Comparing the corank of fine Selmer group and Selmer group of elliptic curves

**Authors**:
Sudhanshu Shekhar

**Author institution:**Department of Mathematics and Statistics, IIT Kanpur, India

**Summary: **
Let p be an odd prime, K ∞ be a pro-p, p-adic Lie extension
of K = Q (μ p) of dimension two containing the cyclotomic
Z p-extension K cyc of K and H be the Galois group of
K/K cyc. Let λ (H) be the Iwasawa algebra over H.
Given an elliptic curve E defined over Q with good and
supersingular reduction at p, we compare the
λ (H)-corank of the fine Selmer group of E over K with
the Iwasawa λ-invariant of the ±-Selmer group of E
over K cyc. Using this, we find examples of elliptic curves
defined over Q with good and supersingular reduction at p
satisfying pseudo nullity conjecture over K ∞.

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