Galois cohomology of elliptic curves over anticyclotomic extensions

2025/08/15 by Dac-Nhan-Tam Nguyen, R. Sujatha, Nguyen, Dac-Nhan-Tam +1 · 1 citation
Computer Science · Mathematics · #11G05 (Primary) 11R23 #11R34 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2508.11835

openalex publication_date 2025/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be an imaginary quadratic field and p be an odd prime number. Let E/ℚ be an elliptic curve with good ordinary reduction at p. We study the Iwasawa theory of E over the anticyclotomic ℤ_p-extension of K by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of E over the unique ℤ_p²-extension of K as well as over the anticyclotomic extension of K.

Citations

• Congruent elliptic curves over some p-adic Lie extensions
• Special values of anticyclcotomic Rankin-Selberg L-functions
• The Heegner point Kolyvagin system
• Iwasawa theory for elliptic curves

Cited by

• On λ-invariants of congruent modular forms in the anticyclotomic, indefinite setting

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• The anticyclotomic main conjectures for elliptic curves
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• On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations