Related papers: 0-Auslander correspondence

The paper concerns a certain subcategory of the category of representations for a semisimple algebraic group $G$ in characteristic $p$, which arise from the semisimple modules for the corresponding quantum group at a $p$-th root of unity.…

These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical…

We continue our study of outer elements of the noncommutative H^p spaces associated with Arveson's subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the…

We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular…

The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of…

Let $\Lambda$ be a finite dimensional algebra. Let $\mathcal C$ be a functorially finite exact subcategory of $\Lambda$-mod with enough projective and injective objects and $\mathcal S (\mathcal C)$ be its monomorphism category. It turns…

For a reductive group $G$ we equip the category of $G_\mathcal{O}$-equivariant polarizable pure Hodge modules on the affine Grassmannian $\mathrm{Gr}_G$ with a structure of neutral Tannakian category. We show that it is equivalent to a…

A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.

Let $A$, $B$ and $C$ be associative rings with identity. Using a result of Koenig we show that if we have a $\mathbb{D}^{{\rm{b}}}({\rm{{mod\mbox{-}}}} )$ level recollement, writing $A$ in terms of $B$ and $C$, then we get a…

We study the equivalences induced by some special silting objects in the derived category over dg-algebra whose positive cohomologies are all zero.

We show that a $KK$-equivalence between two unital $C^*$-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a $\mathbf{K}_*$-equivalence, where $\mathbf{K}_*$ is Waldhausen's…

In this paper some combinatorial and homological tools are used to describe and give an explicit formula for the number of exceptional pairs (exceptional sequences of length two) for some classes of Nakayama Algebras and for the Auslander…

Let $\mathfrak{g}$ be a root-reductive Lie algebra over an algebraically closed field $\mathbb{K}$ of characteristic $0$ with a splitting Borel subalgebra $\mathfrak{b}$ containing a splitting maximal toral subalgebra $\mathfrak{h}$. We…

We give a survey on Auslander-Gorenstein algebras with a focus on finite-dimensional algebras. We put an emphasis on recent classification results for special classes of algebras and the newly discovered interactions of the Auslander-Reiten…

We give an exposition and generalization of Orlov's theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary…

The non-abelian Hodge correspondence is a real analytic map between the moduli space of stable Higgs bundles and the deRham moduli space of irreducible flat connections mediated by solutions to the self-duality equations. In this paper we…

We prove, over any base ring, that the infinity-category of strictly unital A-infinity-categories (and strictly unital functors) is equivalent to the infinity-category of unital A-infinity-categories (and unital functors). We also identify…

We recall the definition of $q$-differential algebras and discuss some representative examples. In particular we construct the $q$-analog of the Hochschild coboundary. We then construct the universal $q$-differential envelope of a unital…

We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a…

We prove that the global Jacquet--Langlands correspondence ${\rm JL}$ for ${\rm GL}(2)$ can be realized via tensor products over Hecke algebras. Let $G$ be a non-split inner form of ${\rm GL}(2)$ over a number field. Using the similitude…