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VOL. 86 | 2020 Anticyclotomic main conjecture for modular forms and integral Perrin-Riou twists
Shinichi Kobayashi, Kazuto Ota

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

Abstract

We prove a one-sided divisibility relation for the anticyclotomic Iwasawa main conjecture for modular forms in terms of the $p$-adic $L$-function constructed by Bertolini-Darmon-Prasanna and Brakočević. The divisibility relation is known by Castella if $p$ is ordinary and by Castella-Wan for the elliptic curve case. Here we prove the higher weight non-ordinary case with a treatment that works uniformly for both ordinary and non-ordinary cases. In the proof, we establish a theory of integral Perrin-Riou twist. It enables us not only to twist systems of generalized Heegner cycles (which are not norm-compatible) by any continuous $p$-adic anticyclotomic characters but also to investigate the denominators of resulting systems explicitly.

Information

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

Digital Object Identifier: 10.2969/aspm/08610537

Subjects:
Primary: 11R23
Secondary: 11F11 , 11G40

Keywords: elliptic modular forms , generalized Heegner cycles , Iwasawa theory

Rights: Copyright © 2020 Mathematical Society of Japan

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