Let $X$ be a quasi separated, quasi compact scheme, $Z$ be a closed subscheme on $X$. We denote by $\hat{X}$ the formal scheme of $X$ along $Z$.

My questions are the following.

(1) How to define the stable infinity category $\text{perf}(\hat{X})$ of perfect complexes on $\hat{X}$. (2) Is there the Grothendieck existence theorem for perfect complexes on $\hat{X}$? i.e, any perfect complex on $\hat{X}$ comes from a perfect complex on $X_n$?

Let $X$ be a quasi separated, quasi compact scheme, $Z$ be a closed subscheme on $X$. We denote by $\hat{X}$ the formal scheme of $X$ along $Z$.

My questions are the following.

(1) How to define the stable infinity category $\text{perf}(\hat{X})$ of perfect complexes on $\hat{X}$. (2) Assume $x$ is proper over an affine scheme $S$. Is there the Grothendieck existence theorem for perfect complexes on $\hat{X}$? i.e, any perfect complex on $\hat{X}$ comes from a perfect complex on $X_n$?