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

Authors From Afeka: Dr. Arielle Leitner

Abstract

We classify Chabauty limits of groups fixed by various (abstract) involutions over SL(2,F), where F is a finite field-extension of Qp, with p≠2. To do so, we first classify abstract involutions over SL(2,F) with F a quadratic extension of Qp, 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 Hθ⊂SL(2,F), where Hθ is the fixed point group of an F-involution θ over SL(2,F).