On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction

Chan Ho Kim

doi:10.1007/978-3-032-13123-2_8

On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction

Chan Ho Kim^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to conference › Conference paper › peer-review

Abstract

In this short note, we study the anticyclotomic analogue of the “weak” main conjecture of Mazur–Tate on Fitting ideals of Selmer groups for elliptic curves with supersingular reduction.

Original language	English
Title of host publication	Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday
Editors	Matteo Longo, Marco Adamo Seveso, Rodolfo Venerucci, Stefano Vigni
Publisher	Springer
Pages	229-240
Number of pages	12
ISBN (Print)	9783032131225
DOIs	https://doi.org/10.1007/978-3-032-13123-2_8
State	Published - 2026
Event	International Conference on Elliptic curves and modular forms in arithmetic geometry. Celebrating Massimo Bertolini's 60th birthday, ECMFAG 2022 - Milano, Italy Duration: 2022.09.12 → 2022.09.16

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	527 PROMS
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Elliptic curves and modular forms in arithmetic geometry. Celebrating Massimo Bertolini's 60th birthday, ECMFAG 2022
Country/Territory	Italy
City	Milano
Period	22.09.12 → 22.09.16

Keywords

11F67
11G40
11R23
Anticyclotomic Iwasawa theory
Refined Iwasawa theory

Access to Document

10.1007/978-3-032-13123-2_8

Cite this

Kim, C. H. (2026). On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction. In M. Longo, M. A. Seveso, R. Venerucci, & S. Vigni (Eds.), Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday (pp. 229-240). (Springer Proceedings in Mathematics and Statistics; Vol. 527 PROMS). Springer. https://doi.org/10.1007/978-3-032-13123-2_8

Kim, Chan Ho. / On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction. Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday. editor / Matteo Longo ; Marco Adamo Seveso ; Rodolfo Venerucci ; Stefano Vigni. Springer, 2026. pp. 229-240 (Springer Proceedings in Mathematics and Statistics).

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title = "On the Anticyclotomic Mazur{\textendash}Tate Conjecture for Elliptic Curves with Supersingular Reduction",

abstract = "In this short note, we study the anticyclotomic analogue of the {\textquotedblleft}weak{\textquotedblright} main conjecture of Mazur{\textendash}Tate on Fitting ideals of Selmer groups for elliptic curves with supersingular reduction.",

keywords = "11F67, 11G40, 11R23, Anticyclotomic Iwasawa theory, Refined Iwasawa theory",

author = "Kim, \{Chan Ho\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.; International Conference on Elliptic curves and modular forms in arithmetic geometry. Celebrating Massimo Bertolini's 60th birthday, ECMFAG 2022 ; Conference date: 12-09-2022 Through 16-09-2022",

year = "2026",

doi = "10.1007/978-3-032-13123-2\_8",

language = "English",

isbn = "9783032131225",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "229--240",

editor = "Matteo Longo and Seveso, \{Marco Adamo\} and Rodolfo Venerucci and Stefano Vigni",

booktitle = "Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday",

}

Kim, CH 2026, On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction. in M Longo, MA Seveso, R Venerucci & S Vigni (eds), Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday. Springer Proceedings in Mathematics and Statistics, vol. 527 PROMS, Springer, pp. 229-240, International Conference on Elliptic curves and modular forms in arithmetic geometry. Celebrating Massimo Bertolini's 60th birthday, ECMFAG 2022, Milano, Italy, 22.09.12. https://doi.org/10.1007/978-3-032-13123-2_8

On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction. / Kim, Chan Ho.
Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday. ed. / Matteo Longo; Marco Adamo Seveso; Rodolfo Venerucci; Stefano Vigni. Springer, 2026. p. 229-240 (Springer Proceedings in Mathematics and Statistics; Vol. 527 PROMS).

Research output: Contribution to conference › Conference paper › peer-review

TY - GEN

T1 - On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction

AU - Kim, Chan Ho

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

PY - 2026

Y1 - 2026

N2 - In this short note, we study the anticyclotomic analogue of the “weak” main conjecture of Mazur–Tate on Fitting ideals of Selmer groups for elliptic curves with supersingular reduction.

AB - In this short note, we study the anticyclotomic analogue of the “weak” main conjecture of Mazur–Tate on Fitting ideals of Selmer groups for elliptic curves with supersingular reduction.

KW - 11F67

KW - 11G40

KW - 11R23

KW - Anticyclotomic Iwasawa theory

KW - Refined Iwasawa theory

UR - https://www.scopus.com/pages/publications/105040591761

U2 - 10.1007/978-3-032-13123-2_8

DO - 10.1007/978-3-032-13123-2_8

M3 - Conference paper

AN - SCOPUS:105040591761

SN - 9783032131225

T3 - Springer Proceedings in Mathematics and Statistics

SP - 229

EP - 240

BT - Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday

A2 - Longo, Matteo

A2 - Seveso, Marco Adamo

A2 - Venerucci, Rodolfo

A2 - Vigni, Stefano

PB - Springer

T2 - International Conference on Elliptic curves and modular forms in arithmetic geometry. Celebrating Massimo Bertolini's 60th birthday, ECMFAG 2022

Y2 - 12 September 2022 through 16 September 2022

ER -

Kim CH. On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction. In Longo M, Seveso MA, Venerucci R, Vigni S, editors, Elliptic Curves and Modular Forms in Arithmetic Geometry - Celebrating Massimo Bertolini's 60th Birthday. Springer. 2026. p. 229-240. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-032-13123-2_8

On the Anticyclotomic Mazur–Tate Conjecture for Elliptic Curves with Supersingular Reduction

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