Mathematical Research Letters

Volume 16 (2009)

Number 3

Analytification is the limit of all tropicalizations

Pages: 543 – 556



Sam Payne (Stanford University)


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.

Published 1 January 2009