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

Abstract

Mazur and Tate proposed a conjecture which compares the Mordell-Weil rank of an elliptic curve over $\mathbb{Q}$ 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.

41 pages

References in corpus (2)

• On the order of vanishing of Stickelberger elements of Hilbert modular forms
• A refined Beilinson-Bloch conjecture for motives of modular forms