Local types of (Γ,G)-bundles and parahoric group schemes

2022/10/05 by Damiolini, Chiara, Hong, Jiuzu
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2210.02379

Abstract

Let G be a simple algebraic group over an algebraically closed field k. Let Γ be a finite group acting on G. We classify and compute the local types of (Γ, G)-bundles on a smooth projective Γ-curve in terms of the first non-abelian group cohomology of the stabilizer groups at the tamely ramified points with coefficients in G. When char(k)=0, we prove that any generically simply-connected parahoric Bruhat--Tits group scheme can arise from a (Γ,G_ad)-bundle. We also prove a local version of this theorem, i.e. parahoric group schemes over the formal disc arise from constant group schemes via tamely ramified coverings.

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