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arXiv · 1311.0502

Skeleta in non-Archimedean and tropical geometry

Andrew W. Macpherson
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Abstract

I describe an algebro-geometric theory of skeleta, which provides a unified setting for the study of tropical varieties, skeleta of non-Archimedean analytic spaces, and affine manifolds with singularities. Skeleta are spaces equipped with a structure sheaf of topological semirings, and are locally modelled on the spectra of the same. The primary result of this paper is that the topological space underlying a non-Archimedean analytic space may locally be recovered from the sheaf of `pointwise valuations' of its analytic functions.

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Andrew W. Macpherson. 2013-11-03. Skeleta in non-Archimedean and tropical geometry. https://arxiv.org/abs/1311.0502

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