On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction

2018/04/02 by Chan-Ho Kim, Kim, Chan-Ho, Masato Kurihara +1 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1804.00418

Abstract

In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic ℤ_p-extension of ℚ of an elliptic curve over ℚ. Especially, we present a proof of the "weak main conjecture" à la Mazur and Tate for elliptic curves with good (supersingular) reduction at an odd prime p. We also prove the "strong main conjecture" suggested by the second named author under the validity of the ±-main conjecture and the vanishing of a certain error term. The key idea is the explicit comparison among "finite layer objects", "±-objects", and "fine objects" in Iwasawa theory. The case of good ordinary reduction is also treated.

Cited by

• Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two
• On the Fitting ideals of anticyclotomic Selmer groups of elliptic curves with good ordinary reduction

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