On the quantitative variation of congruence ideals and integral periods of modular forms

Abstract

We prove the conjecture of Pollack and Weston on the quantitative analysis of the level lowering congruence à la Ribet for modular forms of higher weight. It was formulated and studied in the context of the integral Jacquet-Langlands correspondence and anticyclotomic Iwasawa theory for modular forms of weight two and square-free level for the first time. We use a completely different method based on the $R=\mathbb{T}$ theorem established by Diamond-Flach-Guo and Dimitrov and an explicit comparison of adjoint $L$-values. We briefly discuss arithmetic applications of our main result at the end.

To appear in Research in the Mathematical Sciences

Cited by in corpus (3)

• Indivisibility of Heegner cycles over Shimura curves and Selmer groups
• Wiles defect of Hecke algebras via local-global arguments
• On the Fitting ideals of anticyclotomic Selmer groups of elliptic curves with good ordinary reduction