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arXiv · 2304.03970

The Valuative Section Conjecture, \'Etale Homotopy, and Berkovich Spaces

Jesse Pajwani
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Abstract

We reinterpret a result of Pop and Stix on the $p$-adic section conjecture in terms of Berkovich spaces and fixed points. In doing this, we see a version of the result extends to larger classes of fields, which in turn allows us to prove a valuative section conjecture type result for a larger class of varieties. This adds to the programme to reinterpret anabelian geometry results in terms of \'etale homotopy types.

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Jesse Pajwani. 2023-04-08. The Valuative Section Conjecture, \'Etale Homotopy, and Berkovich Spaces. https://doi.org/10.4310/hha.2025.v27.n2.a12

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