Intersection Theorem for DG-modules

Abstract

Let A be a commutative noetherian local DG-ring with bounded cohomology. The Intersection Theorem for DG-modules is examined and some of its applications are provided. The first is to prove the DG-setting of the amplitude inequality, New Intersection Theorem and Krull's principle ideal theorem. The second is to solve completely the Minamoto's conjecture in [Israel J. Math. 242 (2021) 1-36]. The third is to show the DG-version of the Bass conjecture about Cohen-Macaulay rings and the Vasconcelos conjecture about Gorenstein rings.