On non-trivial Λ-submodules with finite index of the plus/minus Selmer group over anticyclotomic ℤ_p-extension at inert primes

2023/08/31 by Ryota Shii, Shii, Ryota
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2308.16384

openalex publication_date 2023/08/31 · openalex created_date 2023/09/03 · openalex updated_date 2026/07/28

Abstract

Let K be an imaginary quadratic field where p is inert. Let E be an elliptic curve defined over K and suppose that E has good supersingular reduction at p. In this paper, we prove that the plus/minus Selmer group of E over the anticyclotomic ℤ_p-extension of K has no non-trivial Λ-submodules of finite index under mild assumptions for E. This is an analogous result to R. Greenberg and B. D. Kim for the anticyclotomic ℤ_p-extension essentially. By applying the results of A. Agboola--B. Howard or A. Burungale--K. Büyükboduk--A. Lei, we can also construct examples satisfying the assumptions of our theorem.

Related

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• On anticyclotomic Selmer groups of elliptic curves
• Selmer groups and anticyclotomic ℤ_p-extensions II
• On the plus and the minus Selmer groups for elliptic curves at supersingular primes
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