On Derivatives of Kato’s Euler System and the Mazur-Tate Conjecture

David Burns; Takamichi Sano; Masato Kurihara

doi:10.1093/imrn/rnaf012

On Derivatives of Kato’s Euler System and the Mazur-Tate Conjecture

David Burns
, Takamichi Sano
, Masato Kurihara

Osaka City University
Keio University

Research output: Contribution to journal › Article › peer-review

137 Downloads (Pure)

Abstract

We provide a new interpretation of the Mazur-Tate Conjecture and then use
it to obtain the first (unconditional) theoretical evidence in support of the conjecture for elliptic curves of strictly positive rank.

Original language	English
Article number	rnaf012
Number of pages	28
Journal	International Mathematics Research Notices
Volume	2025
Issue number	4
Early online date	14 Feb 2025
DOIs	https://doi.org/10.1093/imrn/rnaf012
Publication status	Published - Feb 2025

Keywords

elliptic curves, Birch-Swinnerton-Dyer Conjecture, Mazur-Tate Conjecture, Kato’s Euler system.

Access to Document

10.1093/imrn/rnaf012Licence: Unspecified

On Derivatives of Kato’s_BURNS_Published14February2025_GREEN_AAM (CC BY)Accepted author manuscript, 582 KBLicence: CC BY

Cite this

@article{3d0372eeea064be894f21f9a4e8fe8e3,

title = "On Derivatives of Kato{\textquoteright}s Euler System and the Mazur-Tate Conjecture",

abstract = "We provide a new interpretation of the Mazur-Tate Conjecture and then use it to obtain the first (unconditional) theoretical evidence in support of the conjecture for elliptic curves of strictly positive rank.",

keywords = "elliptic curves, Birch-Swinnerton-Dyer Conjecture, Mazur-Tate Conjecture, Kato{\textquoteright}s Euler system.",

author = "David Burns and Takamichi Sano and Masato Kurihara",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = feb,

doi = "10.1093/imrn/rnaf012",

language = "English",

volume = "2025",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "4",

}

TY - JOUR

T1 - On Derivatives of Kato’s Euler System and the Mazur-Tate Conjecture

AU - Burns, David

AU - Sano, Takamichi

AU - Kurihara, Masato

PY - 2025/2

Y1 - 2025/2

N2 - We provide a new interpretation of the Mazur-Tate Conjecture and then use it to obtain the first (unconditional) theoretical evidence in support of the conjecture for elliptic curves of strictly positive rank.

AB - We provide a new interpretation of the Mazur-Tate Conjecture and then use it to obtain the first (unconditional) theoretical evidence in support of the conjecture for elliptic curves of strictly positive rank.

KW - elliptic curves, Birch-Swinnerton-Dyer Conjecture, Mazur-Tate Conjecture, Kato’s Euler system.

UR - https://www.scopus.com/pages/publications/85219689199

U2 - 10.1093/imrn/rnaf012

DO - 10.1093/imrn/rnaf012

M3 - Article

SN - 1073-7928

VL - 2025

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 4

M1 - rnaf012

ER -

On Derivatives of Kato’s Euler System and the Mazur-Tate Conjecture

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this