Chabauty limits of groups of involutions in SL(2,F) for local fields

2022/08/25 by Ciobotaru, Corina, Leitner, Arielle
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2208.12247

Abstract

We classify Chabauty limits of groups fixed by various (abstract) involutions over SL(2,F), where F is a finite field-extension of ℚ_p, with p≠ 2. To do so, we first classify abstract involutions over SL(2,F) with F a quadratic extension of ℚ_p, and prove p-adic polar decompositions with respect to various subgroups of p-adic SL₂. Then we classify Chabauty limits of: SL(2, F) ⊂ SL(2,E) where E is a quadratic extension of F, of SL(2,ℝ) ⊂ SL(2,ℂ), and of H_θ⊂ SL(2,F), where H_θ is the fixed point group of an F-involution θ over SL(2,F).

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