Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

A p-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist I 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales mathématiques du Québec Springer Journals

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

Kobayashi, Shinichi
Annales mathématiques du Québec , Volume 47 (1) – Apr 1, 2023
Download PDF
44 pages

Loading next page...
 
/lp/springer-journals/a-p-adic-interpolation-of-generalized-heegner-cycles-and-integral-2RUUqO5PV9
Publisher
Springer Journals
Copyright
Copyright © Fondation Carl-Herz and Springer Nature Switzerland AG 2023. corrected publication 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.. corrected publication 2023
ISSN
2195-4755
eISSN
2195-4763
DOI
10.1007/s40316-023-00213-4
Publisher site
See Article on Publisher Site

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.

Journal

Annales mathématiques du Québec – Springer Journals

Published: Apr 1, 2023

Keywords: Primary 11R23; Secondary 11G40; 11F11; 11G15; 11F67; 11F85

References

  • Anticyclotomic p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adic L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}-function of central critical Rankin-Selberg L-value
    Brakočević, M
  • Kummer theory for abelian varieties over local fields
    Coates, J; Greenberg, R
  • Heegner cycles and p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adic L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}-functions
    Castella, F; Hsieh, M-L
  • Local units modulo circular units
    Coleman, R
  • Higher regulators and Hecke L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}-series of imaginary quadratic fields
    Deninger, C
  • Class groups of abelian fields, and the main conjecture
    Greither, C
  • On the theory of commutative formal groups
    Honda, T
  • The Eisenstein measure and p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adic interpolation
    Katz, N
  • Iwasawa theory for elliptic curves at supersingular primes
    Kobayashi, S
  • The p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adic Gross-Zagier formula for elliptic curves at supersingular primes
    Kobayashi, S
  • Anticyclotomic main conjecture for modular forms and integral Perrin-Riou twists, Advanced Studies in Pure Mathematics, Development of Iwasawa Theory - the Centennial of K
    Kobayashi, S; Ota, K
  • Kolyvagin’s method for Chow groups of Kuga-Sato varieties
    Nekovář, J
  • On the p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adic height of Heegner cycles
    Nekovář, J
  • Fonctions L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adiques, théorie d’Iwasawa et points de Heegner
    Perrin-Riou, B
  • Théorie d’Iwasawa des représentations p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-adiques sur un corps local
    Perrin-Riou, B
  • Théorie d’Iwasawa et loi explicite de réciprocité
    Perrin-Riou, B
  • On the L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}-functions of canonical Hecke characters of imaginary quadratic fields
    Rohrlich, D
  • Motives for modular forms
    Scholl, A
  • On CM abelian varieties over imaginary quadratic fields
    Yang, T
  • On explicit reciprocity law over formal groups
    Zhang, S