Related papers: Finite torsors on projective schemes defined over …

Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable properties. We offer several applications of this technique,…

We study Artin algebras $A$ and commutative Noetherian complete local rings $R$ in connection with the following decomposition property of Gorenstein-projective modules: $(*)$ any Gorenstein-projective module is a direct sum of finitely…

For a finite-dimensional simple Lie algebra $\mathfrak{g}$, we use the vertex tensor category theory of Huang and Lepowsky to identify the category of standard modules for the affine Lie algebra $\hat{\mathfrak{g}}$ at a fixed level…

A Tannakian category is an abelian tensor category equipped with a fiber functor and additional structures which ensure that it is equivalent to the category of representations of some affine groupoid scheme acting on the spectrum of a…

We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.

We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

Let $X$ be a measure space with a measure-preserving action $(g,x) \mapsto g \cdot x$ of an abelian group $G$. We consider the problem of understanding the structure of measurable tilings $F \odot A = X$ of $X$ by a measurable tile $A…

We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept "module (co)end". This tool allows us to give different proofs to several known results…

We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…

The goal of the present paper is to classify an interesting class of elementary quasi-Hopf algebras, or equivalently, finite-dimensional pointed Majid algebras. By a Tannaka-Krein type duality, this determines a big class of pointed finite…

We prove that the category of finitely generated graded modules over the quiver Hecke algebra of arbitrary type admits numerous stratifications in the sense of Kleshchev. A direct consequence is that the full subcategory corresponding to…

In this paper, the projectivity of a finitely generated flat module of a commutative ring is studied through its exterior powers and invariant factors and then various new results are obtained. Specially, the related results of Endo,…

We describe the main questions connected to torsion subgroups in the unit group of integral group rings of finite groups and algorithmic methods to attack these questions. We then prove the Zassenhaus Conjecture for Amitsur groups and prove…

Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$. In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes of rings. We also determine conditions under which…

Let $G$, $G_1$ and $G_2$ be quasi-finite and flat group schemes over a complete discrete valuation ring $R$, $\varphi_1:G\to G_1$ any morphism of $R$-group schemes and $\varphi_2:G\to G_2$ a model map. We construct the pushout $P$ of $G_1$…

We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in…

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the…

In this paper, we establish a structure theorem for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. Our structure theorem contains the solution for Yau's conjecture and it can be regarded as a natural…