I've asked this question here but never got an answer, a simplified version of the question is the following:
Given an intersection of hypersurfaces $Y$ on a smooth projective variety $X$ over a finite field, is the category of vector bundles defined on a neighborhood of the $Y$ equivalent to the category of vector bundles on the formal neighborhood of $Y$ ($\text{dim}Y\geq 2$)? This is asking whether $\text{Leff(Y,X)}$ holds or not (This is true if we work over an algebraically closed field)
This seems to be true in the case of very ample divisors (one hypersurface). This example claims it to be true without assumptions on the field. The example does not claim the extension is unique on the neighborhood, so I am wondering whether an ample divisor $Y$ in a smooth projective variety $X$ of dimension $\geq 3$ satisfies $\text{Leff}(Y,X)$ or not? (field is not algebraically closed)
