In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.

In [BH5] it is shown how the Relative Hurewicz Theorem follows from a Generalised Van Kampen Theorem (GVKT) for the fundamental crossed complex of a filtered space, and in [BL3] it is shown how a new multirelative Hurewicz Theorem follows from a GVKT for the fundamental cat-group of an n-cube of spaces. The purpose of this paper is to advertise and explain some implications and special cases of...

We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of indecomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko states that the category of reflexive toric sheaves is equivalent to the category of vector spaces together with a certain family of filtrations. Within th...

We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of I I -Ulrich modules.

One of the first remarkable results in representation theory artin algebras, due to Auslander and Ringel-Tachikawa, is characterisation when an algebra representation-finite. In this paper, we investigate aspects representation-finiteness general context exact categories sense Quillen. framework, introduce “big objects” prove Auslander-type “splitting-big-objects” theorem. Our approach generali...

We show that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures, using a generalization of the decomposition theorem of Beilinson, Bernstein and Deligne to the case of filtered D-modules. As a corollary, we get the total infinitesimal invariant of a (higher) cycle in a direct sum of t...

For finitely generated module M over a local ring R, the conventional notions of complete intersection dimension CI-dimRM and CohenMacaulay dimension CM-dimRM do not extend to cover the case of infinitely generated modules. In this paper we introduce similar invariants for not necessarily finitely generated modules, (namely, complete intersection flat and Cohen-Macaulay flat dimensions) which f...