Analytification is the limit of all tropicalizations

Details Analytification is the limit of all tropicalizations Analytification is the limit of all tropicalizations

2008-05-13

arxiv.org/abs/0805.1916v3

Math. Res. Lett. 16 (2009), no. 3, 543--556

Mathematics

Algebraic Geometry

13 pages. v3: expository improvements throughout, especially in section 5 on fields with the trivial valuation. added appendix

Scientific paper

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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