Example 52.8.6. In Lemma 52.8.5 we do not know that the inverse systems $H^ i_ J(M/I^ nM)$ satisfy the Mittag-Leffler condition. For example, suppose that $A = \mathbf{Z}_ p[[x, y]]$, $I = (p)$, $J = (p, x)$, and $M = A/(xy - p)$. Then the image of $H^0_ J(M/p^ nM) \to H^0_ J(M/pM)$ is the ideal generated by $y^ n$ in $M/pM = A/(p, xy)$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).