Differential modules with maximal torsion
Let \(R\) be a reduced local analytic \(k\)-algebra, where \(k\) is a field of characteristic zero. It is well known that \(R\) is regular iff its universally finite differential module \(D(R/k)\) is free. A still unsettled conjecture of \textit{R. Berger} [Math. Z. 81, 326-354 (1963; Zbl 0113.263)] states that if \(R\) is one-dimensional then \(R\) is regular if \(D(R/k)\) is torsionfree. The main result of this paper states that Berger's conjecture is true in case \(RDR=DR\) [theorem 3]. This condition is satisfied, e.g., if \(D(R/k)\) has maximal torsion.
scientific article; zbMATH DE number 124274