On the Fitting ideals of anticyclotomic Selmer groups of elliptic curves with good ordinary reduction

2025/05/14 by Kim, Chan-Ho
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.09125

Abstract

We give a short proof of the anticyclotomic analogue of the "strong" main conjecture of Kurihara on Fitting ideals of Selmer groups for elliptic curves with good ordinary reduction under mild hypotheses. More precisely, we completely determine the initial Fitting ideal of Selmer groups over finite subextensions of an imaginary quadratic field in its anticyclotomic ℤ_p-extension in terms of Bertolini--Darmon's theta elements.

Citations

• On the quantitative variation of congruence ideals and integral periods of modular forms
• On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction
• Overconvergent quaternionic forms and anticyclotomic p-adic L-functions
• An anticyclotomic Mazur-Tate conjecture for modular forms
• Special values of anticyclotomic L-functions for modular forms
• Iwasawa theory for elliptic curves

Related

• On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction
• On the anticyclotomic Mazur-Tate conjecture for elliptic curves with supersingular reduction
• Selmer groups and anticyclotomic ℤ_p-extensions II
• Cotorsion of anti-cyclotomic Selmer groups on average
• On non-trivial Λ-submodules with finite index of the plus/minus Selmer group over anticyclotomic ℤ_p-extension at inert primes