Polytopes and simplexes in p-adic fields
Logic
2016-11-15 v2
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.
Cite
@article{arxiv.1602.07209,
title = {Polytopes and simplexes in p-adic fields},
author = {Luck Darnière},
journal= {arXiv preprint arXiv:1602.07209},
year = {2016}
}