# Semi-algebraic triangulation over p-adically closed fields

## TL;DR

This paper establishes a triangulation theorem for semi-algebraic sets over p-adically closed fields, enabling new applications like flexible retractions and splitting, similar to real algebraic geometry.

## Contribution

It introduces a triangulation theorem for semi-algebraic sets over p-adically closed fields, extending real algebraic geometry techniques to the p-adic context.

## Key findings

- Triangulation theorem for semi-algebraic sets over p-adic fields
- Existence of flexible retractions for semi-algebraic sets
- Splitting properties for semi-algebraic sets

## Abstract

We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for semi-algebraic sets.