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arXiv · 2403.13382

Gr{ö}bner bases over polytopal affinoid algebras

Moulay A. Barkatou·Lucas Legrand·Tristan Vaccon
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Abstract

Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry. In this article, we present a theory of Gr{ö}bner bases for polytopal affinoid algebras that extends both Caruso et al.'s theory of Gr{ö}bner bases on Tate algebras and Pauer et al.'s theory of Gr{ö}bner bases on Laurent polynomials. We provide effective algorithms to compute Gr{ö}bner bases for both ideals of Laurent polynomials and ideals in polytopal affinoid algebras. Experiments with a Sagemath implementation are provided.

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Moulay A. Barkatou, Lucas Legrand, Tristan Vaccon. 2025-05-06. Gr{ö}bner bases over polytopal affinoid algebras. https://arxiv.org/abs/2403.13382

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