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Polytopes and simplexes in p-adic fields

Abstract : We introduce topological notions of polytopes and simplexes, the latter being expected to play in p-adically closed fields the role played by real simplexes in the classical results of triangulation of semi-algebraic sets over real closed fields. We prove that the faces of every p-adic polytope are polytopes and that they form a rooted tree with respect to specialisation. Simplexes are then defined as polytopes whose faces tree is a chain. Our main result is a construction allowing to divide every p-adic polytope in a complex of p-adic simplexes with prescribed faces and shapes.
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Contributor : Luck Darnière <>
Submitted on : Saturday, October 22, 2016 - 11:23:42 PM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM


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  • HAL Id : hal-01276748, version 2
  • ARXIV : 1602.07209



Luck Darnière. Polytopes and simplexes in p-adic fields. Annals of Pure and Applied Logic, Elsevier Masson, 2016, 168 (6), pp.1284-1307. ⟨hal-01276748v2⟩



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