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On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting

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Veröffentlicht/Copyright: 26. März 2024
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 37 Heft 1

Abstract

We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form f and an imaginary quadratic field satisfying a “relaxed” Heegner hypothesis. Let Λ be the anticyclotomic Iwasawa algebra. Following the approach of Howard and Longo–Vigni, we construct the Λ-adic Kolyvagin system of generalized Heegner classes coming from Heegner points on a suitable Shimura curve. As its application, we also prove one divisibility relation in the Iwasawa–Greenberg main conjecture for the p-adic L-function defined by Magrone.

Keywords: Modular forms; Shimura curves; Heegner cycles; Selmer groups
MSC 2020: 11F11; 14C25

Communicated by Freydoon Shahidi

Funding statement: The author gratefully acknowledges financial support by Projet KUPSUP RIN Emergent 2022 Region Normandie.

Acknowledgements

We would like to thank Stefano Vigni for helpful discussions on one of his joint works with Matteo Longo, and the anonymous referee for valuable comments and suggestions on an earlier version of the article.

References

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Received: 2023-04-18
Revised: 2024-02-16
Published Online: 2024-03-26
Published in Print: 2025-01-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Some properties of extended frame measure
  3. Orthogonal separation of variables for spaces of constant curvature
  4. Fundamental properties of Cauchy–Szegő projection on quaternionic Siegel upper half space and applications
  5. Uniform bounds for Kloosterman sums of half-integral weight with applications
  6. q-supercongruences from Watson's 8φ7 transformation
  7. Submodules of normalisers in groupoid C*-algebras and discrete group coactions
  8. Explicit bounds for the solutions of superelliptic equations over number fields
  9. The existence of optimal solutions for nonlocal partial systems involving fractional Laplace operator with arbitrary growth
  10. A Kollár-type vanishing theorem for k-positive vector bundles
  11. New sequence spaces derived by using generalized arithmetic divisor sum function and compact operators
  12. On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting
  13. A p-adic analog of Hasse--Davenport product relation involving ϵ-factors
  14. On arithmetic quotients of the group SL2 over a quaternion division k-algebra
  15. Euler’s integral, multiple cosine function and zeta values
  16. Paley inequality for the Weyl transform and its applications
  17. Homogeneous ACM and Ulrich bundles on rational homogeneous spaces
  18. Arithmetic progression in a finite field with prescribed norms
https://doi.org/10.1515/forum-2023-0141
Schlagwörter für diesen Artikel
Modular forms; Shimura curves; Heegner cycles; Selmer groups

Artikel in diesem Heft

  1. Frontmatter
  2. Some properties of extended frame measure
  3. Orthogonal separation of variables for spaces of constant curvature
  4. Fundamental properties of Cauchy–Szegő projection on quaternionic Siegel upper half space and applications
  5. Uniform bounds for Kloosterman sums of half-integral weight with applications
  6. q-supercongruences from Watson's 8φ7 transformation
  7. Submodules of normalisers in groupoid C*-algebras and discrete group coactions
  8. Explicit bounds for the solutions of superelliptic equations over number fields
  9. The existence of optimal solutions for nonlocal partial systems involving fractional Laplace operator with arbitrary growth
  10. A Kollár-type vanishing theorem for k-positive vector bundles
  11. New sequence spaces derived by using generalized arithmetic divisor sum function and compact operators
  12. On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting
  13. A p-adic analog of Hasse--Davenport product relation involving ϵ-factors
  14. On arithmetic quotients of the group SL2 over a quaternion division k-algebra
  15. Euler’s integral, multiple cosine function and zeta values
  16. Paley inequality for the Weyl transform and its applications
  17. Homogeneous ACM and Ulrich bundles on rational homogeneous spaces
  18. Arithmetic progression in a finite field with prescribed norms
Heruntergeladen am 11.5.2026 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2023-0141/html?lang=de
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