Mathematical Research Letters

Volume 16 (2009)

Number 3

Analytification is the limit of all tropicalizations

Pages: 543 – 556

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n3.a13

Author

Sam Payne (Stanford University)

Abstract

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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