Let $p$ be a prime number and let $Y$ over $\mathbb F\_p$ be a Siegel modular variety, with minimal compactification $X$. It is well known that $X^{\operatorname{ord}}$, the ordinary locus of $X$ is affine (since it is cut out by the Hasse invariant, that is a section of an ample line bundle). But what about $Y^{\operatorname{ord}}$, the ordinary locus of $Y$? So the question is the following.


Is the ordinary locus of $Y$ an affine scheme?


Thank you!



Is the ordinary locus affine?
No. It's well known that the complement of a closed subset of codimension two or more in an affine variety is never affine. The minimal compactification has codimension *g*.


