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A p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I

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Abstract

In this paper, we develop an integral refinement of the Perrin-Riou theory of exponential maps. We also formulate the Perrin-Riou theory for anticyclotomic deformation of modular forms in terms of the theory of the Serre–Tate local moduli and interpolate generalized Heegner cycles p-adically.

Résumé

Dans cet article, nous développons un raffinement entier de la théorie des applications exponentielles de Perrin- Riou. Nous formulons également la théorie de Perrin-Riou pour les déformations anticyclotomiques de formes modulaires en utilisant la théorie des modules locaux de Serre- Tate et nous interpolons p-adiquement les cycles de Heegner généralisés.

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Acknowledgements

The author thanks Ashay Burungale and Kazuto Ota for their valuable comments. He also thanks Ming-Lun Hsieh for answering questions for [6]. He is very grateful to the anonymous referees for their sharp comments and appropriate advice, which improved the exposition significantly. A part of the work in this paper was obtained in 2013 and 2014 when the author was visiting Jan Nekovář at Paris 6 University. He would like to dedicate this paper to his memory. He also thanks Henri Darmon, Adrian Iovita and Antonio Lei for giving him the opportunity to publish this paper.

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  1. Faculty of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Shinichi Kobayashi

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  1. Shinichi Kobayashi
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Correspondence to Shinichi Kobayashi.

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This research was supported in part by KAKENHI (25707001, 17H02836, 22H00096)

French abstract corrected.

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Kobayashi, S. A p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I. Ann. Math. Québec 47, 73–116 (2023). https://doi.org/10.1007/s40316-023-00213-4

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