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arXiv:0805.1916 [math.AG]AbstractReferencesReviewsResources

Analytification is the limit of all tropicalizations

Sam Payne

Published 2008-05-13, updated 2009-03-11Version 3

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.

Comments: 13 pages. v3: expository improvements throughout, especially in section 5 on fields with the trivial valuation. added appendix showing that tropicalization is invariant under extensions of valued fields
Journal: Math. Res. Lett. 16 (2009), no. 3, 543--556
Categories: math.AG
Subjects: 32C99, 14G22
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