Equivariant line bundles with connection on the p-adic upper half plane

2023/09/11 by Ardakov, Konstantin, Wadsley, Simon J.
#14F10 #14G22 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2309.05462

Abstract

Let F be a finite extension of ℚ_p, let Ω_F be Drinfeld's upper half-plane over F and let G⁰ the subgroup of GL₂(F) consisting of elements whose determinant has norm 1. By working locally on Ω_F, we construct and classify the torsion G⁰-equivariant line bundles with integrable connection on Ω in terms of the smooth linear characters of the units of the maximal order of the quaternion algebra over F.

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