Journal of the Ramanujan Mathematical Society

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Comparing the Corank of Fine Selmer Group and Selmer Group of Elliptic Curves


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1 Department of Mathematics and Statistics, IIT Kanpur, India
     

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Let p be an odd prime, K∞ be a pro-p, p-adic Lie extension of K = ℚ(μp) of dimension two containing the cyclotomic ℤp-extension Kcyc of K and H be the Galois group of K∞/Kcyc. 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 Kcyc. 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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  • Comparing the Corank of Fine Selmer Group and Selmer Group of Elliptic Curves

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Authors

Sudhanshu Shekhar
Department of Mathematics and Statistics, IIT Kanpur, India

Abstract


Let p be an odd prime, K∞ be a pro-p, p-adic Lie extension of K = ℚ(μp) of dimension two containing the cyclotomic ℤp-extension Kcyc of K and H be the Galois group of K∞/Kcyc. 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 Kcyc. Using this, we find examples of elliptic curves defined over ℚ with good and supersingular reduction at p satisfying pseudo nullity conjecture over K∞.

References