Families of two dimensional modular (φ,Γ)-modules

2024/05/27 by Elmar Große-Klönne, Große-Klönne, Elmar
Mathematics · #11F80 #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2405.17133

openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F/\mathbb Q_p be a finite unramified extension, let k be a finite extension of the residue field of F. We provide explicit constructions of integral structures for all rank two étale Lubin-Tate (φ,\mathcal O_F^×)-modules over k. We construct algebraic families of such integral structures and show that these comprehensively reflect the degeneration behaviour of (φ,\mathcal O_F^×)-modules. These results reveal new combinatorial structures of the moduli stack of (φ,\mathcal O_F^×)-modules, and allow us, in particular, to rederive the fact that the Serre weights assigned to a two dimensional \rm Gal(F/F)-representation over k can be read off from the geometry of the stack.

Related

• Lubin-Tate and multivariable (φ,O_K^×)-modules in dimension 2
• Moduli stacks of Lubin--Tate (φ,Γ)-modules
• Irreducible mod p Lubin-Tate (φ,Γ)-modules
• Iwasawa theory and F-analytic Lubin-Tate (φ,Γ)-modules
• On the rank of the multivariable (φ,O_K^×)-modules associated to mod p representations of GL₂(K)