A formal model of Coleman families and applications to Iwasawa invariants

TL;DR

This paper develops a formal model for Coleman families of modular forms, constructs associated Galois representations, and studies how Iwasawa invariants vary within these families, extending previous results for Hida families.

Contribution

It introduces a formal model for Coleman families and establishes the existence of Galois representations, enabling analysis of Iwasawa invariants in this broader context.

Findings

Construction of a formal model for Coleman families.

Existence proof for associated Galois representations.

Analysis of Iwasawa invariants' variation in Coleman families.

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 $\lambda$- and $\mu$-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.