31 citations · 73 across the 27 of their papers we have counts for
19 papers · 1 filter
Amplitude inequalities for local (co)homology
Lars Winther Christensen, Luigi Ferraro, Henrik Holm
Peskine and Szpiro's Intersection Theorem for finitely generated modules was generalized by Foxby to all modules and bounded complexes of such. We strengthen Foxby's result and pro…
On modules with self Tor vanishing
Olgur Celikbas, Henrik Holm
The long-standing Auslander and Reiten Conjecture states that a finitely generated module over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several auth…
Equivalences from tilting theory and commutative algebra from the adjoint functor point of view
Olgur Celikbas, Henrik Holm
We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a dua…
Approximations by maximal Cohen-Macaulay modules
Henrik Holm
Auslander and Buchweitz have proved that every finitely generated module over a Cohen-Macaulay (CM) ring with a dualizing module admits a so-called maximal CM approximation. In ter…
The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings
Henrik Holm
Over a Cohen-Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences…
The category of maximal Cohen--Macaulay modules as a ring with several objects
Henrik Holm
Over a commutative local Cohen--Macaulay ring, we view and study the category of maximal Cohen--Macaulay modules as a ring with several objects. We compute the global dimension of…
K-groups for rings of finite Cohen-Macaulay type
Henrik Holm
For a local Cohen-Macaulay ring R of finite CM-type, Yoshino has applied methods of Auslander and Reiten to compute the Grothendieck group of the category mod(R) of finitely genera…
Vanishing of cohomology over Cohen--Macaulay rings
Lars Winther Christensen, Henrik Holm
A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings - colloquially called AC rings - that satisfy a natural condition on vanishing of cohomolo…
Construction of totally reflexive modules from an exact pair of zero divisors
Henrik Holm
Let A be a local ring which admits an exact pair x,y of zero divisors as defined by Henriques and Sega. Assuming that this pair is regular and that there exists a regular element o…
Cotorsion pairs induced by duality pairs
Henrik Holm, Peter Jorgensen
We introduce the notion of a duality pair and demonstrate how the left half of such a pair is often covering and preenveloping. As an application, we generalize a result by Enochs…
Beyond Totally Reflexive Modules and Back
Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm
Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory…
Rings without a Gorenstein analogue of the Govorov-Lazard Theorem
Henrik Holm, Peter Jorgensen
It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective…
Foxby equivalence over associative rings
Henrik Holm, Diana White
We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C.…
Compactly generated homotopy categories
Henrik Holm, Peter Jørgensen
Over an associative ring we consider a class of left modules which is closed under set-indexed coproducts and direct summands. We investigate when the triangulated hom…
Cotorsion pairs associated with Auslander categories
Edgar E. Enochs, Henrik Holm
We prove that the Auslander class determined by a semidualizing module is the left half of a perfect cotorsion pair. We also prove that the Bass class determined by a semidualizing…
Ascent Properties of Auslander Categories
Lars Winther Christensen, Henrik Holm
Let R be a homomorphic image of a Gorenstein local ring. Recent work has shown that there is a bridge between Auslander categories and modules of finite Gorenstein homological dime…
Semi-dualizing modules and related Gorenstein homological dimensions
Henrik Holm, Peter Jorgensen
A semi-dualizing module over a commutative noetherian ring A is a finitely generated module C with RHom_A(C,C) \simeq A in the derived category D(A). We show how each such module g…
Cohen-Macaulay injective, projective, and flat dimension
Henrik Holm, Peter Jorgensen
We define three new homological dimensions - Cohen-Macaulay injective, projective, and flat dimension - which inhabit a theory similar to that of classical injective, projective, a…
On Gorenstein Projective, Injective and Flat Dimensions - A Functorial Description with Applications
L. Winther Christensen, A. Frankild, H. Holm
Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules o…