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

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 ${\mathbb{Z}}_p$-extension in terms of Bertolini--Darmon's theta elements.

arXiv commentThe refereed version. To appear in Canadian Mathematical Bulletin

References in corpus (4)

• On the anticyclotomic Iwasawa main conjecture for modular forms
• On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction
• On the quantitative variation of congruence ideals and integral periods of modular forms
• On the Fitting ideals of anticyclotomic Selmer groups of elliptic curves with good ordinary reduction

Cited by in corpus (1)

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