A formal model of Coleman families and applications to Iwasawa invariants

2023/03/27 by Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Di Capriglio, Filippo Alberto Edoardo Nuccio Mortarino Majno, Tadashi Ochiai +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.14940

openalex publication_date 2023/03/27 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

Abstract

For a given Coleman family of modular forms, we construct a formal modeland prove the existence of a family of Galois representations associated to the Colemanfamily. As an application, we study the variations of Iwasawa λ- and μ-invariants of dualfine (strict) Selmer groups over the cyclotomic Zp-extension of Q in Coleman families ofmodular forms. This generalizes an earlier work of Jha and Sujatha for Hida families.

Related

• Iwasawa Main Conjecture for p-adic families of elliptic modular cuspforms
• Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families
• On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations
• Integral Iwasawa theory of Galois representations for non-ordinary primes
• Fine Selmer groups of modular forms