Related papers: Homology of FI-modules

We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We…

The main theorem of Church-Ellenberg [arXiv:1506.01022] is a sharp bound on the homology of FI-modules, showing that the Castelnuovo-Mumford regularity of FI-modules over Z can be bounded in terms of generators and relations. We give a new…

We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This implies a linear stable range for the homology of congruence…

We give bounds for various homological invariants (including Castelnuovo-Mumford regularity, degrees of local cohomology, and injective dimension) of finitely generated VI-modules in the non-describing characteristic case. It turns out that…

We give refined bounds for the regularity of FI-modules and the stable ranges of FI-modules for various forms of their stabilization studied in the representation stability literature. We show that our bounds are sharp in several cases. We…

We establish bounds for the Castelnuovo-Mumford regularity of a finitely generated graded module and its symmetric powers in terms of the degrees of the generators of the module and the degrees of their relations. We extend to modules (and…

Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and number of generators of the two graded modules involved.…

We show that the FI-homology of an FI-module can be computed via a Koszul complex. As an application, we prove that the Castelnuovo-Mumford regularity of a finitely generated torsion FI-module is equal to its degree.

An upper bound for the Castelnuovo-Mumford regularity of the associated graded module of an one-dimension module is given in term of its Hilbert coeffcients. It is also investigated when the bound is attained.

We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-modules (namely the local degree and regularity, together with the stable…

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for…

The asymptotic stability of several homological invariants of the graded pieces of a graded module has attracted quite a lot of attention over the last decades. We provide in this text several stability results together with estimates of…

Let $R$ be a standard graded algebra over a field $k$. We prove an Auslander-Buchsbaum formula for the absolute Castelnuovo-Mumford regularity, extending important cases of previous works of Chardin and R\"omer. For a bounded complex of…

In this paper we show how, given a complex of graded modules and knowing some partial Castelnuovo-Mumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity…

We give bounds on the Castelnuovo-Mumford regularity of the associated graded module of an arbitrary good filtration and of its fiber cone. These bounds extend previous results of Rossi-Trung-Valla and Linh.

We show that the Eisenbud-Goto conjecture holds for (homogeneous) seminormal simplicial affine semigroup rings. Moreover, we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the…

We explore a theory of depth for FI_G-modules which are presented in finite degrees. Using this theory, we prove results about the regularity, and provide novel bounds on stable ranges of FI-modules, making effective a theorem of Nagpal and…

In this article we extend a previous definition of Castelnuovo-Mumford regularity for modules over an algebra graded by a finitely generated abelian group. Our notion of regularity is based on Maclagan and Smith's definition, and is…

We give two kinds of bounds for the Castelnuovo-Mumford regularity of the canonical module and the deficiency modules of a ring, respectively in terms of the homological degree and the Castelnuovo-Mumford regularity of the original ring.

In this paper we use a homological approach to obtain upper bounds for a few homological invariants of $FI_G$-modules $V$. These upper bounds are expressed in terms of the generating degree and torsion degree, which measure the top and…