ALGORITHMIC METHODS IN THE CONSTRUCTION OF GENERAL NERON DESINGULARIZATION

Abstract

Let A ! A0 be a regular morphism of Noetherian rings,any A-morphism v : B ! A0 with B an A-algebra of finite type,factors through a smooth A-algebra C, that is v is a composite A-morphism B ! C ! A0. The A-algebra C is called a General Neron Desingularization. In this thesis we give a uniform General Neron Desingularization for one dimen- sional local rings with respect to morphisms which coincide modulo a high power of themaximalideal.TheresulthasinterestingapplicationsinthecaseofCohen- Macaulay rings. Moreover, as our another contribution,we give an easy proof of the General Neron Desingularization in the frame of regular morphisms between Artinianlocal rings and Noetherian local rings of dimension one. We also give algorithms to construct theN´eron Desingularization in different cases.