The Nash-Tognoli theorem over the rationals and its version for isolated singularities

Riccardo Ghiloni, Enrico Savi

Let $\mathbb{Q}$ be the field of rational numbers and let $X$ be a subset of ${\mathbb{R}}^n$. We say that $X$ is $\mathbb{Q}$-algebraic if it is the common zero set in $\mathbb{R}^n…