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

2025/10/14 by Dac-Nhan-Tam Nguyen, Nguyen, Dac-Nhan-Tam
Mathematics · #11R23 (Primary) 11G40 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2510.12890

openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We give a precise, computable formula for comparing λ-invariants between modular forms in the anticyclotomic indefinite setting where the Selmer groups have positive rank. This is an improvement of Hatley-Lei \citeHL19, HL21 where the authors give a formula with incomputable error terms.

Citations

• Galois cohomology of elliptic curves over anticyclotomic extensions
• On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions
• Residual supersingular Iwasawa theory and signed Iwasawa invariants
• Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms
• Variation of anticyclotomic Iwasawa invariants in Hida families
• Iwasawa theory for elliptic curves

Related

• Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms
• The vanishing of anticyclotomic μ-invariants for non-ordinary modular forms
• On a parity result for the symmetric square of modular forms with congruent residual representations
• Modular forms via invariant theory
• λ-invariant stability in families of modular Galois representations