Analytification is the limit of all tropicalizations
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2008
- DOI:
- 10.48550/arXiv.0805.1916
- arXiv:
- arXiv:0805.1916
- Bibcode:
- 2008arXiv0805.1916P
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 32C99;
- 14G22
- E-Print:
- 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