相关论文: Singular equivalence and the (Fg) condition
The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an…
An algebra $A$ is left weakly Gorenstein if any semi-Gorenstein-projective left $A$-modules is Gorenstein-projective. The weakly Gorensteinness of two kinds of algebras are answered. Using the method of the monomorphism category, it is…
We extend the basic theory of the coniveau and strong coniveau filtrations to the $\ell$-adic setting. By adapting the examples of Benoist--Ottem to the $\ell$-adic context, we show that the two filtrations differ over any algebraically…
A relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Dual version will be treated. Several examples and applications will be provided. In particular, we show that under certain…
We study the hyperbolicity of singular quotients of bounded symmetric domains. We give effective criteria for such quotients to satisfy Green-Griffiths-Lang's conjectures in both analytic and algebraic settings. As an application, we show…
We prove the categorical form of Fargues' geometrization conjecture for $\mathrm{GL}_n$ along $L$-parameters of Langlands-Shahidi type for rational, torsion, and integral coefficients. Additionally, we prove that in this case the…
We extend some recent work of D. McCarthy, proving relations among some Fourier coefficients of a degree 2 Siegel modular form $F$ with arbitrary level and character, provided there are some primes $q$ so that $F$ is an eigenform for the…
We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…
Hirotaka Fujimoto considered two meromorphic maps $ f $ and $ g $ of $\mathbb{C}^m $ into $\mathbb{P}^n $ such that $ f^*(H_j)=g^*(H_j)$ ($ 1\leq j\leq q $) for $ q $ hyperplanes $ H_j $ in $\mathbb{P}^n $ in general position and proved $…
We identify a class of singular algebraic foliations whose leaves through singular points retain regularity. The proof consists in showing existence of residual gerbes for certain formal stacks, which do not enjoy smooth presentations. As…
We characterize Morita equivalence of theories in the sense of Johnstone in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson for cartesian, regular, coherent, geometric and first-order…
Let $A$ and $B$ be two Morita equivalent finite dimensional associative algebras over a field $\Bbbk$. It is well known that Hochschild cohomology is invariant under Morita equivalence. Since infinitesimal deformations are connected with…
This paper is investigative work into the properties of a family of graded algebras recently defined by Varagnolo and Vasserot, which we call VV algebras. We compare categories of modules over KLR algebras with categories of modules over VV…
In this paper, we classify the singular parameters for the Birman-Murakami-Wenzl algebra over an arbitrary field. Equivalently, we give a criterion for the Birman-Murakami-Wenzl algebra being Morita equivalent to the direct sum of the Hecke…
We prove two results from Morita theory of stable model categories. Both can be regarded as topological versions of recent algebraic theorems. One is on recollements of triangulated categories, which have been studied in the algebraic case…
We introduce group graded basic Morita equivalences between algebras deter- mined by blocks of normal subgroups, and by using the extended Brauer quotient, we show that they induce graded basic Morita equivalences at local levels.
We investigate level $p$ Eisenstein congruences for GSp$_4$, generalisations of level $1$ congruences predicted by Harder. By studying the associated Galois and automorphic representations we see conditions that guarantee the existence of a…
Let $A$ be a unital separable non-elementary amenable simple stably finite C*-algebra such that its tracial state space has a $\sigma$-compact countable-dimensional extremal boundary. We show that $A$ is ${\cal Z}$-stable if and only if it…
We introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of…
We introduce a generalization of tilting modules of finite projective dimension, projectively Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ext-perpendicular categories. Under a certain finiteness…