Gr{\"o}bner bases over Tate algebras
Algebraic Geometry
2019-01-29 v1 Symbolic Computation
Number Theory
Abstract
Tate algebras are fundamental objects in the context of analytic geometry over the p-adics. Roughly speaking, they play the same role as polynomial algebras play in classical algebraic geometry. In the present article, we develop the formalism of Gr{\"o}bner bases for Tate algebras. We prove an analogue of the Buchberger criterion in our framework and design a Buchberger-like and a F4-like algorithm for computing Gr{\"o}bner bases over Tate algebras. An implementation in SM is also discussed.
Cite
@article{arxiv.1901.09574,
title = {Gr{\"o}bner bases over Tate algebras},
author = {Xavier Caruso and Tristan Vaccon and Thibaut Verron},
journal= {arXiv preprint arXiv:1901.09574},
year = {2019}
}