3 problems

Let $(R,\mathfrak{m})$ be a regular local ring, and let $\mathfrak{p}$ and $\mathfrak{q}$ be prime ideals in $R$ such that … Here $\mathfrak{p}^{(n)}$ denotes the $n$th symbolic po…

Let $w,\tau\in W/W_{P_d}$. Let $R^+$ and $R_{P_d}^+$ denote the positive roots of the ambient root system and of the parabolic subsystem, respectively. Define $S'_{w,\tau}$ to be t…

Bhatt–Hochster–Ma conjecture. The ring $R$ has a lim Cohen–Macaulay sequence.