相关论文: Twisted support varieties

For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism f is equal to the number of finite-dimensional fixed points of the induced map f^…

The class of support $\tau$-tilting modules was introduced to provide a completion of the class of tilting modules from the point of view of mutations. In this article we study $\tau$-tilting finite algebras, i.e. finite dimensional…

We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…

Let $(\mbox{mod} \Lambda',\mbox{mod} \Lambda,\mbox{mod} \Lambda'')$ be a recollement of abelian categories for artin algebras $\Lambda'$, $\Lambda$ and $\Lambda''$. Under certain conditions, we present an explicit construction of gluing of…

We study cohomology support loci of regular holonomic D-modules on complex abelian varieties, and obtain conditions under which each irreducible component of such a locus contains a torsion point. One case is that both the D-module and the…

We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct…

Let $G$ be a finite group and $T(G)$ be the sum of the degrees of its irreducible complex representations. We investigate the relationship between $T(G)$ and the number of twisted involutions $m_\sigma = |\{g \in G \mid \sigma(g) =…

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

The main result of this paper is a combinatorial description of a basis of standard level 1 module for the twisted affine Lie algebra $A_2^{(2)}.$ This description also gives two new combinatorial identities of G\"ollnitz (or…

We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linear abelian monoidal category we obtain a graded…

A classical twisting lemma says that given a finitely generated torsion module $M$ over the Iwasawa algebra $\mathbb{Z}_p[[\Gamma ]]$ with $\Gamma \cong \mathbb{Z}_p, \ \exists$ a continuous character $\theta: \Gamma \rightarrow…

In this article, we study and review some aspects of twisted cohomologies on algebraic and analytic varieties. We compared such cohomologies in both the algebraic and analytic categories and defined two types of twisting parameters in the…

We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples,…

We define support varieties in an axiomatic setting using the prime spectrum of a lattice of ideals. A key observation is the functoriality of the spectrum and that this functor admits an adjoint. We assign to each ideal its support and can…

Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…

We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms. We also discuss how…

We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven…

It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can exist. In particular,…

We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…

We introduce mixed twistor $D$-modules, and establish the fundamental functorial property. We also prove that they are described as the gluing of admissible variations of mixed twistor structure. In a sense, mixed twistor $D$-modules could…