Let Y_{i} be infinitely many reduced closed subschemes of a smooth scheme X over an algebraically closed field. Suppose that they have a point y in common and y is closed in X. Let Z be the intersection of Y_{i}'s in X. What is the relation between Spf(hat{Z}{y}) and Spf(\hat{Y{i}}_{y})? Here, \hat{A}{a} refers to the completed stalk and Spf denotes the formal spectrum.

Let $Y_{i}$ be infinitely many reduced closed subschemes of a smooth scheme $X$ over an algebraically closed field. Suppose that they have a point $y$ in common and $y$ is closed in $X$. Let $Z$ be the intersection of $Y_{i}$'s in $X$. What is the relation between $\operatorname{Spf}(\hat{Z}_{y})$ and $\operatorname{Spf}(\hat{\left(Y_{i}\right)}_{y})$? Here, $\hat{A}_{a}$ refers to the completed stalk and $\operatorname{Spf}$ denotes the formal spectrum.

Let Y_{i} be infinitely many reduced closed subschemes of a smooth scheme X over an algebraically closed field. Suppose that they have a point y in common and y is closed in X. Let Z be the intersection of Y_{i}'s in X. What is the relation between Spf(hat{Z}{y}) and Spf(\hat{Y{i}}_{y})? Here, \hat{A}{a} refers to the completed stalk.

Let Y_{i} be infinitely many reduced closed subschemes of a smooth scheme X over an algebraically closed field. Suppose that they have a point y in common and y is closed in X. Let Z be the intersection of Y_{i}'s in X. What is the relation between Spf(hat{Z}{y}) and Spf(\hat{Y{i}}_{y})? Here, \hat{A}{a} refers to the completed stalk and Spf denotes the formal spectrum.