Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms

2017/06/14 by Jeffrey Hatley, Antonio Lei, Hatley, Jeffrey +1 · 1 citation
Mathematics · #11F11 #11R18 #11R23 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1706.04531

openalex publication_date 2017/06/14 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28

Abstract

We study the variation of Iwasawa invariants of the anticyclotomic Selmer groups of congruent modular forms under the Heegner hypothesis. In particular, we show that even if the Selmer groups we study may have positive coranks, the mu-invariant vanishes for one modular form if and only if it vanishes for the other, and that their lambda-invariants are related by an explicit formula. This generalizes results of Greenberg-Vatsal for the cyclotomic extension, as well as results of Pollack-Weston and Castella-Kim-Longo for the anticyclotomic extension when the Selmer groups in question are cotorsion.

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• On λ-invariants of congruent modular forms in the anticyclotomic, indefinite setting

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