p-adic Hodge parameters in the crystalline representations of GSp4

2025/12/04 by Han, Xiaozheng
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.05275

Abstract

This article gives a generalization of the work of Y.Ding in the context of GSp₄(ℚ_p), where p is an odd prime number. Let ρ be a 4-dimensional generic non-critical crystalline representations of the absolute Galois group of ℚ_p of regular Hodge-Tate weights which is valued in GSp₄(E), where E is a finite extension of ℚ_p, we associate to ρ an explicit locally analytic E-representation π_min(ρ) of GSp₄(ℚ_p), which encodes enough information to determines ρ. Moreover, under certain settings, this construction follows the local-global compatibility.

Citations

• Zariski density of crystalline points on \GSp_2n-valued local deformation rings
• Cohomology of arithmetic families of (phi,Gamma)-modules
• On Jordan-Hölder series of some locally analytic representations
• On the infinite fern of Galois representations of unitary type
• Une correspondance de Jacquet-Langlands p-adique
• Banach space representations and Iwasawa theory

Related

• p-adic Hodge parameters in the crystabelline representations of GL_n
• Hodge filtration and crystalline representations of GL_n
• p-adic Hodge parameters in the crystabelline representations of GL₃(ℚ_p)
• Reductions of Crystalline Representations for Small Weights
• Reductions of Some Crystalline Representations in the Unramified Setting