Related papers: Quantum tilting modules over local rings

Let $\mathfrak F$ be a locally compact nonarchimedean field with residue characteristic $p$ and $G$ the group of $\mathfrak{F}$-rational points of a connected split reductive group over $\mathfrak{F}$. We define a torsion pair in the…

In this note we introduce and study basic properties of two types of modules over a commutative noetherian ring $R$ of positive prime characteristic. The first is the category of modules of finite $F$-type. These objects include reflexive…

We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories.…

Let $\mathfrak g$ be a simple complex Lie algebra. In this paper we study the BGG category $\mathcal O_q$ for the quantum group $U_q(\mathfrak g)$ with $q$ being a root of unity in a field $K$ of characteristic $p >0$. We first consider the…

For each compact, simple, simply-connected Lie group and each integer level we construct a modular tensor category from a quotient of a certain subcategory of the category of representations of the corresponding quantum group. We determine…

We prove that the quantum moduli algebra associated to a possibly punctured compact oriented surface and a complex semisimple Lie algebra $\mathfrak{g}$ is a Noetherian and finitely generated ring. If the surface has punctures, we prove…

Let R be a commutative Noetherian local ring, and denote by mod R the category of finitely generated R-modules. In this paper, we consider when mod R has a nontrivial extension-closed subcategory. We prove that this is the case if there are…

We show the existence of geometric quotients for the spaces of certain classes of morphisms of sheaves on projective space, modulo the canonical action of the group of automorphisms.

Let $\Lambda$ be a left and right noetherian ring and $\mod \Lambda$ the category of finitely generated left $\Lambda$-modules. In this paper we show the following results: (1) For a positive integer $k$, the condition that the subcategory…

Given a closed smooth manifold M which carries a positive scalar curvature metric, one can associate an abelian group P(M) to the space of positive scalar curvature metrics on this manifold. The group of all diffeomorphisms of the manifold…

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…

We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

In this paper, motivated by a work of Luk and Yau, and Huneke and Wiegand, we study various aspects of the cohomological rigidity property of tensor product of modules over commutative Noetherian rings. We determine conditions under which…

We show the existence of tilting objects in the singularity category $\mathsf{D}_{\mathsf{ Sg}}^{\mathsf{ gr}}(eAe)$ associated to certain noetherian AS-regular algebras $A$ and idempotents $e$. This gives a triangle equivalence between…

In this paper we study Category $\mcal O$ for the polynomial toroidal Lie algebras and its $S,H$ type subalgebras. We classify irreducible objects of category $\mcal O$ as unique irreducble quotient of standard modules. Surprisingly,…

The concept of Faltings' local-global principle for the in dimension $< n$ of local cohomology modules over a Noetherian ring $R$ is introduced, and it is shown that this principle holds at levels 1, 2. We also establish the same principle…

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space $W$,…

Let C be a triangulated category with a Serre functor S and X a non-zero contravariantly finite rigid subcategory of C. Then X is cluster tilting if and only if the quotient category C/X is abelian and S(X)=X[2]. As an application, this…

In this paper, by assuming a faithful action of a finite flat $\mathbb{Z}_p$-algebra $\mathscr{R}$ on a $p$-divisible group $\mathcal{G}$ defined over the ring of $p$-adic integers $\mathscr{O}_K$, we construct a category of new…