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Gr{ö}bner bases over Tate algebras (1901.09574v1)
Published 28 Jan 2019 in math.AG, cs.SC, and math.NT
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.