A fundamental theorem is proved for tropical PDEs over valued fields, with the corollary that radii of convergence for ODE solutions can be computed tropically.
Analytification is the limit of all tropicalizations
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We introduce extended tropicalizations for closed subvarieties of toric varieties and show that the analytification of a quasprojective variety over a nonarchimedean field is naturally homeomorphic to the inverse limit of the tropicalizations of its quasiprojective embeddings.
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The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations
A fundamental theorem is proved for tropical PDEs over valued fields, with the corollary that radii of convergence for ODE solutions can be computed tropically.