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Limits of tropicalizations

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Abstract

We give general criteria under which the limit of a system of tropicalizations of a scheme over a nonarchimedean field is homeomorphic to the analytification of the scheme. As an application, we show that the analytification of an arbitrary closed subscheme of a toric variety is naturally homeomorphic to the limit of its tropicalizations, generalizing an earlier result of the third author for quasiprojective varieties.

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Authors and Affiliations

  1. Mathematics Department, University of Michigan, 530 Church Street, Ann Arbor, MI, 48109-1043, USA

    Tyler Foster

  2. Mathematisches Institut, FHeinrich-Heine-Universität, Universitätsstr. 1, 402225, Dsseldorf, Germany

    Philipp Gross

  3. Mathematics Department, Yale University, 10 Hillhouse Ave, New Haven, CT, 06511, USA

    Sam Payne

Authors
  1. Tyler Foster
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  2. Philipp Gross
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  3. Sam Payne
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Correspondence to Tyler Foster.

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Foster, T., Gross, P. & Payne, S. Limits of tropicalizations. Isr. J. Math. 201, 835–846 (2014). https://doi.org/10.1007/s11856-014-1051-x

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  • DOI: https://doi.org/10.1007/s11856-014-1051-x

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