A criterion of Cohen Macaulayness of the form module

Abstract

Let $\mathfrak{𝔮}$ be an ideal of a Noetherian local ring $(A,\mathfrak{𝔪})$ and $M$ a nonzero finitely generated $A$-module. We present a criterion of Cohen–Macaulayness of the form module $G_M(\mathfrak{𝔮})$ in terms of (non)vanishing of a variation of local cohomology introduced by P. Schenzel and the author (J. Commut. Algebra 12:3 (2020), 353-370).