On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting

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Main Author: Pati, Maria Rosaria
Format: Preprint
Published: 2023
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_version_ 1866929268148142080
author Pati, Maria Rosaria
author_facet Pati, Maria Rosaria
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2304_08934
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting
Pati, Maria Rosaria
Number Theory
11R23, 11F11
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.
title On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting
topic Number Theory
11R23, 11F11
url https://arxiv.org/abs/2304.08934