Moduli of p-adic representations of a profinite group

2017/09/13 by António, Jorge
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.04275

Abstract

Let X be a smooth and proper scheme over an algebraically closed field. The purpose of the current text is twofold. First, we construct the moduli stack parametrizing rank n continuous p-adic representations of the étale fundamental group π₁^\textrmét(X). Our construction realizes such object as a ℚ_p-analytic stack, denoted LocSys_p,n (X). Secondly, we prove that LocSys_p,n(X) admits a canonical derived structure. This derived structure allow us to intrinsically recover the deformation theory of continuous p-adic representations, studied in [GV18]. Our proof of geometricity of LocSys_p,n(X) uses in an essential way the ℚ_p-analytic analogue of Lurie-Artin representability, proved in [PY17].

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