Weakly localising subcategories of coherent sheaves and isomorphisms in codimension two

I will consider a weakly localising Serre subcategory $B$ in an abelian category $A$, i.e. a Serre subcategory such that the quotient $A/B$ admits a torsion pair with the torsion-free part equivalent to the category $E$ of $B$-closed objects. I will give sufficient conditions for $B$ to be weakly localising in terms of torsion-tilting chains in $A$. I will also argue that $T$-consistent pairs of t-structures of amplitude 2 are equivalent to (strongly) torsion-tilting chains. Given a scheme $X$ of dimension $n$, the derived category $\mathrm{D}(X)$ admits a $T$-consistent pair of t-structures of amplitude $n$ which yields a pair of amplitude 2. As a result, the category $\mathrm{Coh}_2(X)$ of sheaves supported in codimension 2 is weakly localising. I will prove that, under additional assumptions on $X$, the additive category $E_2(X)$ of locally $\mathrm{Coh}_2(X)$-closed objects allows us to reconstruct $X$ up to an isomorphism outside of codimension 2. For a normal surface $X$ I will construct its final model $X'$ from the additive category $E_2(X)$. I will argue that $X$ admits an open embedding into $X'$ with complement of codimension two and I will give conditions under which $X$ is isomorphic to $X'$. This is based on a joint work with A. Bondal.