The Structure of the Category of Sheaves in the Flat Topology Over Certain Local Rings

Abstract

Introduction. The local rings, A, of the totle are complete, neotherian, local rings of dimension 0, [3, Th. 2] proved useful in the theory of cohomological dimension. By characterizing the etale sheaves (see ? 1) over a special local ring (Th. 1), we are able to further generalize these structure theorems to obtain the canonical decomposition of a sheaf over such a ring into infinitesimal and etale parts, (Th. 2). Hopefully, our structure theorem will help in the investigation of cohomological phenomena over special local rings.