2 problems

Let $(R, \mathfrak m=(x_1,\dots,x_d))$ be a complete $d$-dimensional regular local ring, let $J=(x_1^{a_1},\dots,x_d^{a_d})$ with $a_i>0$, and let $\mathfrak a$ be an $\mathfrak m$…

BCM-rationality conjecture. $R$ is BCM-rational if and only if $R$ has rational singularities.