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.
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.
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