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Preprint Number 1029
1029. Luck Darnière Polytopes and simplexes in p-adic fields E-mail: Submission date: 23 February 2016 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. Mathematics Subject Classification: Keywords and phrases: |
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