Related papers: Tensor product of dualizing complexes over a field

We show that a tensor product of nonexceptional type Kirillov--Reshetikhin (KR) crystals is isomorphic to a direct sum of Demazure crystals; we do this in the mixed level case and without the perfectness assumption, thus generalizing a…

Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of…

The notions of $\mathbb Q$-Gorenstein scheme and of $\mathbb Q$-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of…

There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the tensor nilpotence of morphisms of perfect complexes over…

We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…

Let $H$ be the quantum double of a Nichols algebra of diagonal type. We compute the $R$-matrix of 3-uples of modules for general finite-dimensional highest weight modules over $H$. We calculate also a multiplicative formula for the…

In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known…

We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein…

We prove that for Noetherian, smooth, separated, integral, finite type schemes $X$ and $Y$ over an excellent Dedekind domain $R$, that are properly birational over $R$, we have $R^if_{*}\mathcal{O}_X \cong R^ig_{*} \mathcal{O}_Y$ and $R^i…

In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic…

We show that in Grayson's model of higher algebraic $K$-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev's model for $K_1$ to…

Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and satisfies the condition Hom_R(C,C) \cong R. We prove that a Cohen-Macaulay ring R with dualizing module D admits a…

This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the…

We construct a higher level analogue of Dorey's rule, which describe certain surjective morphisms between Kirillov--Reshetikhin (KR) modules over quantum affine algebras. Building on this, we establish a generalized T-system of short exact…

We establish a characterization of dualizing modules among semidualizing modules. Let R be a finite dimensional commutative Noetherian ring with identity and C a semidualizing R-module. We show that C is a dualizing R-module if and only if…

Let $Y$ be a normal and projective variety over an algebraically closed field $k$ and $V$ a vector bundle over $Y$. We prove that if there exist a $k$-scheme $X$ and a finite surjective morphism $g:X\to Y$ that trivializes $V$ then $V$ is…

We discuss dualisable objects in minimal subcategories of compactly generated tensor triangulated categories, paying special attention to the derived category of a commutative noetherian ring. A cohomological criterion for detecting these…

In 2008, Rogalski and Zhang showed that if R is a strongly noetherian connected graded algebra over an algebraically closed field, then R has a canonical birationally commutative factor. This factor is, up to finite dimension, a twisted…

Let $k$ be a field and let $\Lambda$ be a finite dimensional $k$-algebra. We prove that every bounded complex $V^\bullet$ of finitely generated $\Lambda$-modules has a well-defined versal deformation ring $R(\Lambda,V^\bullet)$ which is a…

Among the finitely generated modules over a Noetherian ring R, the semidualizing modules have been singled out due to their particularly nice duality properties. When R is a normal domain, we exhibit a natural inclusion of the set of…