On the real Section Conjecture in \'etale homotopy theory

We study the Section Conjecture in \'etale homotopy theory for varieties over $\mathbb{R}$. We prove its pro-$2$ variant for equivariantly triangulable varieties. Examples include all smooth varieties as well as all (possibly singular) affine/projective varieties. Building on this, we derive the real Section Conjecture in the geometrically \'etale nilpotent (e.g. simply connected) case.