On wonderful compactifications of $SL(2,F)$ for non-Archimedean local fields $F$

TL;DR

This paper computes and analyzes the wonderful compactifications of symmetric varieties of SL(2,F) over non-Archimedean local fields, identifying stabilizers and comparing them to known Chabauty limits.

Contribution

It provides explicit descriptions of wonderful compactifications for SL(2,F) over certain non-Archimedean fields and compares stabilizers to existing Chabauty limits.

Findings

Explicit descriptions of compactifications for SL(2,F)

Identification of stabilizers of accumulation points

Comparison with Chabauty limits from prior work

Abstract

We compute the wonderful compactification of symmetric varieties of $SL(2,F)$, where $F$ is a finite field-extension of $Q_p$ with $p\neq 2$, that comes from either an abstract or $F$-involutions of $SL(2,F)$. For each of those wonderful compactifications we find the $SL(2,F)$-stabilizers of the accumulation points of the corresponding symmetric varieties and compare them to the Chabauty limits found in Ciobotaru--Leitner 2022.