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Skeleta in non-Archimedean and tropical geometry
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 431-506.

Je décris une théorie algèbro-géometrique de squelettes, qui fournit une cadre unifiée pour l’étude de variétés tropicaux, les squelettes des variétés analytiques non Archimediennes, et les variétés différentielles avec structure affine singulier. Ces squelettes sont des espaces munies d’un faisceau structural de semianneaux topologiques, et sont localement isomorphes aux spectres de ceux-ci. Le résultat principal de cet article dit que l’espace topologique sous-jacent d’une variété analytique non-Archimedienne peut être localement reconstruit par les sections du faisceau de valuations “point-par-point” de ses fonctions analytiques.

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 X underlying a non-Archimedean analytic space may locally be recovered from the sections of the sheaf |𝒪 X | of pointwise valuations of its analytic functions; in other words, (X,|𝒪 X |) is a skeleton.

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DOI : https://doi.org/10.5802/afst.1637
@article{AFST_2020_6_29_2_431_0,
     author = {Andrew W. Macpherson},
     title = {Skeleta in non-Archimedean and tropical geometry},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {431--506},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {2},
     year = {2020},
     doi = {10.5802/afst.1637},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1637/}
}
Andrew W. Macpherson. Skeleta in non-Archimedean and tropical geometry. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 431-506. doi : 10.5802/afst.1637. https://afst.centre-mersenne.org/articles/10.5802/afst.1637/

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