On the Lambda-cotorsion subgroup of the Selmer group

2018/12/01 by Matar, Ahmed
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1812.00207

Abstract

Let E be an elliptic curve defined over a number field K with supersingular reduction at all primes of K above p. If K_∞/K is a ℤ_p-extension such that E(K_∞)[p^∞] is finite and H²(G_S(K_∞), E[p^∞])=0, then we prove that the Λ-torsion subgroup of the Pontryagin dual of Sel_p^∞(E/K_∞) is pseudo-isomorphic to the Pontryagin dual of the fine Selmer group of E over K_∞. This is the Galois-cohomological analog of a flat-cohomological result of Wingberg.

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