On the real Section Conjecture in \'etale homotopy theory
Abstract
We study the Section Conjecture in \'etale homotopy theory for varieties over 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.
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