3 problems

Let $R$ be a Cohen--Macaulay ring, let $\mathfrak{p}$ be a prime ideal of finite projective dimension, and let $\mathrm G=\bigoplus_{t\geq 0}\mathfrak{p}^t/\mathfrak{p}^{t+1}$ be t…

Divisor class group conjecture. The divisor class group of $R_G(d)$ is

The orbit classification conjecture. Two $G$-orbits $\mathcal{O}$ and $\mathcal{O}'$ lie in the same $\mathrm{Aut}(X)^0$-orbit if and only if