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- W2216638845 abstract "In this paper, we provide an overview of recent progress on the interplay between tropical geometry and non-archimedean analytic geometry in the sense of Berkovich. After briefly discussing results by Baker et al. (Algebr. Geom. 3, 63–105 (2016); Contemporary Mathematics, vol 605, pp 93–121. American Mathematical Society, Providence, 2013) in the case of curves, we explain a result from Cueto et al. (Math. Ann. 360, 391–437 (2014)) comparing the tropical Grassmannian of planes to the analytic Grassmannian. We also give an overview of most of the results in Gubler et al. (Adv. Math. 294, 150–215 (2016)), where a general higher-dimensional theory is developed. In particular, we explain the construction of generalized skeleta in Gubler et al. (Adv. Math. 294, 150–215 (2016)) which are polyhedral substructures of Berkovich spaces lending themselves to comparison with tropicalizations. We discuss the slope formula for the valuation of rational functions and explain two results on the comparison between polyhedral substructures of Berkovich spaces and tropicalizations." @default.
- W2216638845 created "2016-06-24" @default.
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- W2216638845 date "2016-01-01" @default.
- W2216638845 modified "2023-09-23" @default.
- W2216638845 title "Analytification and Tropicalization Over Non-archimedean Fields" @default.
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- W2216638845 doi "https://doi.org/10.1007/978-3-319-30945-3_6" @default.
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