# Auslander bounds and homological conjectures.

@article{Wei2008AuslanderBA, title={Auslander bounds and homological conjectures.}, author={Jiaqun Wei}, journal={Revista Matematica Iberoamericana}, year={2008}, volume={27}, pages={871-884} }

Inspired by recent works on rings satisfying Auslander’s conjecture, we study invariants, called Auslander bounds, and prove that they have strong relations to some homological conjectures.

#### 10 Citations

Tilting complexes and Auslander–Reiten conjecture

- Mathematics
- 2012

We studied the properties of tilting complexes and proved that derived equivalences preserve the validity of the Auslander–Reiten conjecture.

Auslander-Reiten conjecture and Auslander-Reiten duality

- Mathematics
- 2013

Abstract Motivated by a result of Araya, we extend the Auslander–Reiten duality theorem to Cohen–Macaulay local rings. We also study the Auslander–Reiten conjecture, which is rooted in Nakayamaʼs… Expand

On the Generalized Auslander–Reiten Conjecture under Certain Ring Extensions

- Mathematics
- Canadian Mathematical Bulletin
- 2015

Abstract We show that under some conditions a Gorenstein ring $R$ satisfies the Generalized Auslander–Reiten conjecture if and only if $R\left[ x \right]$ does. When $R$ is a local ring we prove the… Expand

Derived invariance by syzygy complexes

- Mathematics
- Mathematical Proceedings of the Cambridge Philosophical Society
- 2017

Abstract We study derived invariance through syzygy complexes. In particular, we prove that syzygy-finite algebras and Igusa--Todorov algebras are invariant under derived equivalences. Consequently,… Expand

Derived categories and syzygies

- Mathematics
- 2011

We introduce syzygies for derived categories and study their properties. Using these, we prove the derived invariance of the following classes of artin algebras: (1) syzygy-finite algebras, (2)… Expand

On the Auslander–Reiten conjecture for Cohen–Macaulay rings and path algebras

- Mathematics
- 2017

ABSTRACT In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of d-th… Expand

The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings.

- Mathematics
- 2020

The Auslander-Reiten conjecture is a notorious open problem about the vanishing of Ext modules. In a Cohen-Macaulay local ring $R$ with a parameter ideal $Q$, the Auslander-Reiten conjecture holds… Expand

Auslander-Reiten conjecture for non-Gorenstein Cohen-Macaulay rings

- Mathematics
- 2019

Let $R$ be a Cohen-Macaulay local ring and $Q$ be a parameter ideal of $R$. Due to M. Auslander, S. Ding, and \O. Solberg, the Auslander-Reiten conjecture holds for $R$ if and only if it holds for… Expand

When the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module

- Mathematics
- Journal of Algebra
- 2019

Abstract In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module. Applications go in three directions. The first is to characterize… Expand

Complete cohomology for extriangulated categories

- Mathematics
- 2020

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. In this paper, we study complete cohomology of objects in… Expand

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Local Limitations of the Ext Functor Do Not Exist

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