Reconstruction of a surface from the category of reflexive sheaves.

I discuss the category Ref(X) of reflexive sheaves on a normal Cohen-Macaulay surface X. I describe the canonical structure of an exact category on Ref(X). I introduce the notion of the right abelian envelope of an exact category and use it to reconstruct a surface proper over an affine scheme from the category of reflexive sheaves on it. It is a joint work in progress with A. Bondal.