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arXiv · 2510.13325

On the real Section Conjecture in \'etale homotopy theory

Tim Holzschuh
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Abstract

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.

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Tim Holzschuh. 2025-10-15. On the real Section Conjecture in \'etale homotopy theory. https://arxiv.org/abs/2510.13325

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