Geometric translations of (φ,Γ)-modules for GL₂(ℚ_p)

2024/05/26 by Wu, Zhixiang
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.16637

Abstract

We study ``change of weights'' maps between loci of the stack of (φ,Γ)-modules over the Robba ring with integral Hodge-Tate-Sen weights. We show that in the GL₂(ℚ_p) case these maps can realize translations of (φ,Γ)-modules geometrically. The motivation is to investigate translations of locally analytic representations under the categorical p-adic Langlands correspondence.

Related

• Change of weights for locally analytic representations of \rmGL₂(ℚ_p)
• Arithmetic families of (φ, Γ)-modules and locally analytic representations of GL₂(Q_p)
• (φ,Γ)-modules over relatively discrete algebras
• La correspondance de Langlands locale p-adique pour GL₂(Q_p)
• Towards the wall-crossing of locally ℚ_p-analytic representations of GL_n(K) for a p-adic field K