Approximate liftings in local algebra and a theorem of Grothendieck

Let A and B denote local rings such that A=B/tB, where t is a regular nonunit, and let b denote an ideal in B such that the A-ideal a=b/(t) has codimension greater-or-equal, slanted2. Let F be a reflexive OX-module, where image. Under suitable conditions on A and B and assuming that image and image, it is shown in this article that the dual sheaf Fv can be extended to a reflexive coherent OY-module, where image. The infinitesimal procedure that leads to this sheaf extension makes use of the injective theory of sheaves. Applications to homomorphisms of divisor class groups come about as a consequence of this result, and a strong connection with Grothendieckʹs theorem on parafactoriality is drawn.