On the real Section Conjecture in étale homotopy theory

Abstract

We study the Section Conjecture in étale 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 étale nilpotent (e.g. simply connected) case.

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