相关论文: Finite domination and Novikov rings. Laurent polyn…

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x]. Then C is R-finitely dominated, ie, homotopy equivalent over R to a bounded chain complex of finitely generated…

Let L be a strongly Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent, over L_0, to a bounded complex of finitely generated…

Let C be a bounded cochain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x,y,1/y]. The complex C is called R-finitely dominated if it is homotopy equivalent over R to a bounded complex of finitely…

Let $R$ be a strongly $\mathbb{Z}^2$-graded ring, and let $C$ be a bounded chain complex of finitely generated free $R$-modules. The complex $C$ is $R_{(0,0)}$-finitely dominated, or of type FP over $R_{(0,0)}$, if it is chain homotopy…

Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes…

A finitely generated module over the ring L=Z[t, t^{-1}] of integer Laurent polynomials that has no Z-torsion is determined by a pair of sub-lattices of L^d. Their indices are the absolute values of the leading and trailing coefficients of…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…

Let R be a strongly Z-graded ring with degree-0 subring S, and let C be a chain complex of modules over the subring P of elements of non-negative degree. We show that there are non-commutative localisations of P which detect whether the…

We consider a non-standard totalisation functor to produce a cochain complex from a given double complex: instead of sums or products, totalisation is defined via truncated products of modules. We give an elementary proof of the fact that a…

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring,…

New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension,…

We investigate the similarities between adic finiteness and homological finiteness for chain complexes over a commutative noetherian ring. In particular, we extend the isomorphism properties of certain natural morphisms from homologically…

It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective…

In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

Let $R$ be a commutative noetherian ring, and let $C$ be a semidualizing $R$-module. In this paper, we study levels of bounded complexes of finitely generated $R$-modules with respect to the full subcategory $\mathsf{G}_{C}(R)$ consisting…

We give an algebraic construction of standard modules (infinite dimensional modules categorifying the PBW basis of the underlying quantized enveloping algebra) for Khovanov-Lauda-Rouquier algebras in all finite types. This allows us to…

In this paper we study the properties of the finite topology on the dual of a module over an arbitrary ring. We aim to give conditions when certain properties of the field case are can be still found here. Investigating the correspondence…