Let $P$ be a prime ideal of a Cohen-Macaulay ring $R$. Then is the sequence $\operatorname{depth}(R/P^n)$ eventually constant ?



For every prime ideal $P$ of any Cohen-Macaulay ring $R$, is the sequence $\operatorname{depth}(R/P^n)$ eventually constant?
Yes, for any ideal in a Noetherian local ring. See: [this paper](https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/asymptotic-nature-of-the-analytic-spread/4B358F7CA56A22C1298A57229A7BFA69).


