---
_id: '66358'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Affine Bruhat–Tits buildings are
    geometric spaces extracting the combinatorics of algebraic groups. The building
    of  parameterizes flags of subspaces/lattices in or, equivalently, norms on a
    fixed finite‐dimensional vector space, up to homothety. It has first been studied
    by Goldman and Iwahori as a piecewise‐linear analogue of symmetric spaces. The
    space of seminorms compactifies the space of norms and admits a natural surjective
    restriction map from the Berkovich analytification of projective space that factors
    the natural tropicalization map. Inspired by Payne's result that the analytification
    is the limit of all tropicalizations, we show that the space of seminorms is the
    limit of all tropicalized <jats:italic>linear</jats:italic> embeddings  and prove
    a faithful tropicalization result for compactified linear spaces. The space of
    seminorms is in fact the tropical linear space associated to the universal realizable
    valuated matroid.</jats:p>
article_number: e12850
author:
- first_name: Luca
  full_name: Battistella, Luca
  last_name: Battistella
- first_name: Kevin
  full_name: Kühn, Kevin
  last_name: Kühn
- first_name: Arne
  full_name: Kuhrs, Arne
  last_name: Kuhrs
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Alejandro
  full_name: Vargas, Alejandro
  last_name: Vargas
citation:
  ama: Battistella L, Kühn K, Kuhrs A, Ulirsch M, Vargas A. Buildings, valuated matroids,
    and tropical linear spaces. <i>Journal of the London Mathematical Society</i>.
    2023;109(1). doi:<a href="https://doi.org/10.1112/jlms.12850">10.1112/jlms.12850</a>
  apa: Battistella, L., Kühn, K., Kuhrs, A., Ulirsch, M., &#38; Vargas, A. (2023).
    Buildings, valuated matroids, and tropical linear spaces. <i>Journal of the London
    Mathematical Society</i>, <i>109</i>(1), Article e12850. <a href="https://doi.org/10.1112/jlms.12850">https://doi.org/10.1112/jlms.12850</a>
  bibtex: '@article{Battistella_Kühn_Kuhrs_Ulirsch_Vargas_2023, title={Buildings,
    valuated matroids, and tropical linear spaces}, volume={109}, DOI={<a href="https://doi.org/10.1112/jlms.12850">10.1112/jlms.12850</a>},
    number={1e12850}, journal={Journal of the London Mathematical Society}, publisher={Wiley},
    author={Battistella, Luca and Kühn, Kevin and Kuhrs, Arne and Ulirsch, Martin
    and Vargas, Alejandro}, year={2023} }'
  chicago: Battistella, Luca, Kevin Kühn, Arne Kuhrs, Martin Ulirsch, and Alejandro
    Vargas. “Buildings, Valuated Matroids, and Tropical Linear Spaces.” <i>Journal
    of the London Mathematical Society</i> 109, no. 1 (2023). <a href="https://doi.org/10.1112/jlms.12850">https://doi.org/10.1112/jlms.12850</a>.
  ieee: 'L. Battistella, K. Kühn, A. Kuhrs, M. Ulirsch, and A. Vargas, “Buildings,
    valuated matroids, and tropical linear spaces,” <i>Journal of the London Mathematical
    Society</i>, vol. 109, no. 1, Art. no. e12850, 2023, doi: <a href="https://doi.org/10.1112/jlms.12850">10.1112/jlms.12850</a>.'
  mla: Battistella, Luca, et al. “Buildings, Valuated Matroids, and Tropical Linear
    Spaces.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 1, e12850,
    Wiley, 2023, doi:<a href="https://doi.org/10.1112/jlms.12850">10.1112/jlms.12850</a>.
  short: L. Battistella, K. Kühn, A. Kuhrs, M. Ulirsch, A. Vargas, Journal of the
    London Mathematical Society 109 (2023).
date_created: 2026-07-08T08:04:28Z
date_updated: 2026-07-08T08:04:43Z
doi: 10.1112/jlms.12850
intvolume: '       109'
issue: '1'
language:
- iso: eng
publication: Journal of the London Mathematical Society
publication_identifier:
  issn:
  - 0024-6107
  - 1469-7750
publication_status: published
publisher: Wiley
status: public
title: Buildings, valuated matroids, and tropical linear spaces
type: journal_article
user_id: '82981'
volume: 109
year: '2023'
...