3 problems

Geometric-height conjecture. Over the nonnoetherian locus $\operatorname{Max}S\setminus U_{S/R}$, one has

Prime-norm global-dimension conjecture. If

Let $\mathbb{I}_n$ be the algebra of polynomial integro-differential operators and let $\mathbb{A}_n$ be the corresponding Jacobian algebra. Write ${\rm gldim}(R)$ for the common l…