Related papers: The singularity category and duality for complete …

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

We study the structure of mod 2 cohomology rings of oriented Grassmannians $\tilde{\operatorname{Gr}}_k(n)$ of oriented $k$-planes in $\mathbb{R}^n$. Our main focus is on the structure of the cohomology ring ${\rm…

We generalize the modular Koszul duality of Achar-Riche to the setting of Soergel bimodules associated to any finite Coxeter system. The key new tools are a functorial monodromy action and wall-crossing functors in the mixed modular derived…

We classify the localizing tensor ideals of the integral stable module category for any finite group $G$. This results in a generic classification of $\mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular case…

We prove a Koszul duality theorem between the category of weight modules over the quantized Coulomb branch (as defined by Braverman, Finkelberg and Nakajima) attached to a group $G$ and representation $V$ and a category of $G$-equivariant…

Let $A$ be an augmented differential graded algebra over a field $k$ of characteristic zero, and let $A^!=\mathbf{R}\mathrm{Hom}_A(k,k)$ be its Koszul dual algebra. Blumberg and Mandell showed that, under some finiteness conditions of $A$,…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

Let $\Lambda$ be a finite-dimensional algebra with finite global dimension, $R_k=K[X]/(X^k)$ be the $\mathcal{Z}$-graded local ring with $k\geq1$, and $\Lambda_k=\Lambda\otimes_K R_k$. We consider the singularity category…

Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…

We study H. Dao's invariant $\eta_c^R$ of pairs of modules defined over a complete intersection ring $R$ of codimension $c$ having an isolated singularity. Our main result is that $\eta_c^R$ vanishes for all pairs of modules when $R$ is a…

We show that if $\Lambda$ is a $n$-Koszul algebra and $E=E(\Lambda)$ is its Yoneda algebra, then there is a full subcategory $\mathcal{L}_E$ of the category $Gr_E$ of graded $E$-modules, which contains all the graded $E$-modules presented…

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…

Let $A$, $B$ be two rings and $T=\left(\begin{smallmatrix} A & M \\ 0 & B \\\end{smallmatrix}\right)$ with $M$ an $A$-$B$-bimodule. We first construct a semi-complete duality pair $\mathcal{D}_{T}$ of $T$-modules using duality pairs in…

In this paper, we examine the class of cofibrant modules over a group algebra $kG$, that were defined by Benson in [2]. We show that this class is always the left-hand side of a complete hereditary cotorsion pair in the category of…

In this work we study a kind of coherence condition on FI_G-modules, which generalizes the usual notion of finite generation. We prove that a module is coherent, in the appropriate sense, if and only if its generators, as well as its…

We define and investigate a class of Koszul quasi-hereditary algebras for which there is a natural equivalence between the bounded derived category of graded modules and the bounded derived category of graded modules over (a proper version…

We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor,…

A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…

Let $G$ be a finite group and let $k$ be a sufficiently large finite field. Let $R(G)$ denote the character ring of $G$ (i.e. the Grothendieck ring of the category of ${\mathbb{C}}G$-modules). We study the structure and the representations…

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise…