2 problems

Maximal-set realization conjecture. For every set of ideals $J_1,\ldots,J_s\in\textnormal{\textsf{S}}_{p(t)}^{n}$ such that

Pardue's conjecture. The $\mathbb{N}$-graded Betti table of $I(S\otimes_{\mathbb Z}\ell)$ is independent of $\operatorname{char}\ell$ (equivalently, of $\ell$) for all fields…