VOL. 86 | 2020 Iwasawa theory for modular forms
Xin Wan

Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji

Adv. Stud. Pure Math., 2020: 61-78 (2020) DOI: 10.2969/aspm/08610061


In this paper we give an overview of some aspects of Iwasawa theory for modular forms. We start with the classical formulation in terms of $p$-adic $L$-functions in the ordinary case and the $\pm$-formulation for supersingular elliptic curves. Then we discuss some recent progresses in the proof of the corresponding Iwasawa main conjectures formulated by Kato (Conjecture 4.1), which relates the index of his zeta element to the characteristic ideal of the strict Selmer groups.


Published: 1 January 2020
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.2969/aspm/08610061

Primary: 11R23

Keywords: BSD conjecture , Iwasawa theory , modular forms

Rights: Copyright © 2020 Mathematical Society of Japan


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