Kato's Euler system and the Mazur-Tate refined conjecture of BSD type

2015/09/02 by Kazuto Ota, Ota, Kazuto · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1509.00682

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Mazur and Tate proposed a conjecture which compares the Mordell-Weil rank of an elliptic curve over ℚ with the order of vanishing of Mazur-Tate elements, which are analogues of Stickelberger elements. Under some relatively mild assumptions, we prove this conjecture. Our strategy of the proof is to study divisibility of certain derivatives of Kato's Euler system.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem
• A refined Beilinson-Bloch conjecture for motives of modular forms

Cited by

• The refined Tamagawa number conjectures for GL₂

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