Higher Auslander Correspondence for Dualizing R-Varieties

An Auslander-buchsbaum Identity for Semi- Dualizing Modules

Cluster Tilting for Higher Auslander Algebras

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n-Auslander-Reiten translation functor τn plays an important role in the study of n-cluster tilting subcategories. We study the category Mn of preinjective-like modules obtained by applying τn to injective modules repeatedly. We call a f...

Correspondence homomorphisms for singular varieties

In this paper, Y and X will be (reduced) projective complex varieties. Homology will be singular homology of underlying topological spaces with Z-coefficients, unless specifically signalled otherwise. If Y is smooth and connected and if Z is an effective algebraic cycle in Y ×X equidimensional of dimension r over Y , then the fundamental class [Z] ∈ H2m+2r(Y × X) determines a homomorphism in ho...

Krichever correspondence for algebraic varieties

In the work is constructed new acyclic resolutions of quasicoherent sheaves. These resolutions is connected with multidimensional local fields. Then the obtained resolutions is applied for a construction of generalization of the Krichever map to algebraic varieties of any dimension. This map gives in the canonical way two k -subspaces B ⊂ k((z1)) . . . ((zn)) and W ⊂ k((z1)) . . . ((zn)) ⊕r fro...

Tensor Products and Higher Auslander-reiten Theory

Article history: Received 8 July 2015 Received in revised form 22 February 2016 Available online 4 August 2016 Communicated by S. Koenig We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama give in [6] a criterion for when the tensor product of an n-representation finite algebra and an m-representation ...