How to Tropicalize a non-Archimedean Lattice
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909959588937728 |
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| author | Maazouz, Yassine El |
| author_facet | Maazouz, Yassine El |
| contents | The tropicalization of a linear space over a non-archimedean field is a tropical linear space. In this paper, we present a method for computing the tropicalization of any lattice over a valuation ring. The resulting tropical semimodule is the support of a polyhedral complex constructed from a certain multilinear polynomial we call the entropy polynomial. The key idea in our argument is the tropicalization of Haar measures on lattices over local fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How to Tropicalize a non-Archimedean Lattice Maazouz, Yassine El Combinatorics 14T90, 14T15 The tropicalization of a linear space over a non-archimedean field is a tropical linear space. In this paper, we present a method for computing the tropicalization of any lattice over a valuation ring. The resulting tropical semimodule is the support of a polyhedral complex constructed from a certain multilinear polynomial we call the entropy polynomial. The key idea in our argument is the tropicalization of Haar measures on lattices over local fields. |
| title | How to Tropicalize a non-Archimedean Lattice |
| topic | Combinatorics 14T90, 14T15 |
| url | https://arxiv.org/abs/2512.12127 |