It is a well-known result of Auslander and Reiten that contravariant finiteness the class P ∞ fin (of finitely generated modules finite projective dimension) over an Artin algebra sufficient condition for validity finitistic dimension conjectures. Motivated by fact dimensions can alternatively be computed Gorenstein dimension, we examine in this work counterpart Auslander–Reiten condition, name...

Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but the geometric meaning of the resulting structures is still relatively poorly understood. We discuss here the weighted projective analogs of homogeneous spaces such as the Grassmannian Gr(2, 5) and ort...

In this paper we give a criterion for a left Gorenstein algebra to be AS-regular. Let A be a left Gorenstein algebra such that the trivial module Ak admits a finitely generated minimal free resolution. Then A is AS-regular if and only if its left Gorenstein index is equal to− inf{i |ExtA A (k, k)i = 0}. Furthermore, A is Koszul AS-regular if and only if its left Gorenstein index is depthAA = − ...

We recall the basic geometric properties of the projective variety Latn r (K) parametrizing a family of special lattices over Witt vectors proved in [Hab05, HS, San04]. They are ’Schubert varieties’ in the analog of the affine Grassmannian for G = SL(n) over a complete local field of mixed characteristic, and are normal and Gorenstein [HS]. In this paper, we prove that there exists a set of sub...