Relative liftings
Here is the author's abstract: ``Let \((\Lambda,m)\) be a complete Cohen-Macaulay local ring, \(x\) a system of parameters of \(\Lambda\), and \(M\) a finite \(\bar\Lambda:=\Lambda/(x)\)-module. If Ext\(^2_{\bar\Lambda}(M,M)=0\) then there exists a maximal Cohen-Macaulay \(\Lambda\)-module \(L\) such that \(L/xL\cong M\) by a result of Auslander-Ding-Solberg. Here we investigate the problem of finding a generalized Cohen-Macaulay \(\Lambda\)-module \(T\) such that \(T/xT\cong M\). If \(\Lambda\) is regular and \((x)\not=m\), then we hope that our procedure can be useful for some bundle constructions.'' The author develops a theory of weaker forms of liftability than Auslander-Ding-Solberg's: relative, relative\(^\star\) liftability, etc., including infinitesimal versions. The author proves existence theorems for such liftings, and provides examples of modules which are relative\(^\star\) liftable but not liftable.
scientific article; zbMATH DE number 897493
scientific article