Kato’s Euler System and the Mazur-tate Refined Conjecture of Bsd Type

نویسنده

  • KAZUTO OTA
چکیده

Mazur and Tate proposed a conjecture which compares the Mordell-Weil rank of an elliptic curve overQwith 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. CONTENTS

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A refined conjecture of Mazur-Tate type for Heegner points

In [MT1], B. Mazur and J. Tate present a “refined conjecture of Birch and Swinnerton-Dyer type” for a modular elliptic curve E. This conjecture relates congruences for certain integral homology cycles on E(C) (the modular symbols) to the arithmetic of E over Q. In this paper we formulate an analogous conjecture for E over suitable imaginary quadratic fields, in which the role of the modular sym...

متن کامل

An Elementary Proof of the Mazur-tate-teitelbaum Conjecture for Elliptic Curves

We give an elementary proof of the Mazur-TateTeitelbaum conjecture for elliptic curves by using Kato’s element. 2000 Mathematics Subject Classification: 11F85, 11G05, 11G07, 11G40, 11S40.

متن کامل

A “BSD-type” Conjecture of Mazur and Tate

1 Overview 1.1 Vague form of the conjecture Let E be an elliptic curve over Q. I am going to describe a conjecture of Mazur and Tate which is in some sense a sequel of their investigation (together with Teitelbaum) of a “p-adic BSD conjecture”. However, while this conjecture involves some ideas in the spirit of p-adic L-functions, it is of a completely different nature. There will be an input i...

متن کامل

An Elementary Proof of the Mazur-Tate-Teitelbaum Conjecture for Elliptic Curves Dedicated to Professor John Coates on the occasion of his sixtieth birthday

We give an elementary proof of the Mazur-TateTeitelbaum conjecture for elliptic curves by using Kato’s element. 2000 Mathematics Subject Classification: 11F85, 11G05, 11G07, 11G40, 11S40.

متن کامل

The Birch and Swinnerton-Dyer conjectural formula and visibility Project description

A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure. In many cases, the Birch and Swinnerton-Dyer conjecture (henceforth abbreviated BSD conjecture) predicts the existence of such solutions and describes some of their structure without actually finding the solutions. The imp...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016