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

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.

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