0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 1. χ-functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 2. BPS rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 2.1. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 2.2. Remarks . . . . . . . . . . . . . . . . . . . . . ....

We give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [H. Krause, Approximations and adjoints in homotopy categories, Math. Ann. 353 (2012), 765–781]. Then we provide a criterion for the existence of r...

We study the concept of liaison addition for codimension two subschemes of an arithmetically Gorenstein projective scheme. We show how it relates to liaison and biliaison classes of subschemes and use it to investigate the structure of Gorenstein liaison equivalence classes, extending the known theory for complete intersection liaison of codimension two subschemes. In particular, we show that o...

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1 free module, or R is Gorenstein and an isolated singularity (if R is complete, then it is even a simple hypersurface singularity). The crux of our proof is to...

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then characterize it in terms of the U -resolution dimension of some special injective modules and the property of the functors Ext(Ext(−, U), U) preserving monomorphisms, which develops a classical result of Auslander....

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...

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then characterize it in terms of the U -resolution dimension of some special injective modules and the property of the functors Exti(Exti(−, U), U) preserving monomorphisms, which develops a classical result of Auslande...

Abstract. The conjecture on roots of Ehrhart polynomials, stated by Matsui et al. [15, Conjecture 4.10], says that all roots α of the Ehrhart polynomial of a Gorenstein Fano polytope of dimension d satisfy − d 2 ≤ Re(α) ≤ d 2 − 1. In this paper, we observe the behaviors of roots of SSNN polynomials which are a wider class of the polynomials containing all the Ehrhart polynomials of Gorenstein F...

Given a homomorphism of commutative noetherian rings R → S and an S–module N , it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals sup {m ∈ Z | TorRm(E,N) 6= 0}, where E is the injective hull of the residue field of R. This r...

Auslander’s depth formula for pairs of Tor-independent modules over a regular local ring, depth(M ⊗R N) = depth M + depth N − depthR, has been generalized in several directions; most significantly it has been shown to hold for pairs of Tor-independent modules over complete intersection rings. In this paper we establish a depth formula that holds for every pair of Tate Tor-independent modules ov...