Related papers: Reduction techniques of singular equivalences

Let $X$ be a compact K\"ahler manifold. Given a big cohomology class $\{\theta\}$, there is a natural equivalence relation on the space of $\theta$-psh functions giving rise to $\mathcal S(X,\theta)$, the space of singularity types of…

Let $\mathbf{k}$ be a field of arbitrary characteristic, let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra, and let $V$ be an indecomposable finitely generated non-projective Gorenstein-projective left $\Lambda$-module whose stable…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

This work is an attempt towards a Morita theory for stable equivalences between self-injective algebras. More precisely, given two self-injective algebras A and B and an equivalence between their stable categories, consider the set S of…

We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our decomposition formula can be expressed in terms of a…

For an in invertible quasihomogeneous singularity $w$ we prove an all-genus mirror theorem establishing an isomorphism between two cohomological field theories. On the $B$-side it is the Saito-Givental theory given by a certain choice of a…

We establish a Morita theorem to construct triangle equivalences between the singularity categories of (commutative and non-commutative) Gorenstein rings and the cluster categories of finite dimensional algebras over fields, and more…

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…

We study proof techniques for bisimilarity based on unique solution of equations. We draw inspiration from a result by Roscoe in the denotational setting of CSP and for failure semantics, essentially stating that an equation (or a system of…

We show that a bimodule between block algebras which has a fusion stable endopermutation module as a source and which induces Morita equivalences between centralisers of nontrivial subgroups of a defect group induces a stable equivalence of…

We introduce the notion of combinatorial type of varieties $X$ which generalizes the concept of the dual complex of SNC divisors. It is a unique, up to homotopy, finite simplicial complex $\Sigma(X)$ which is functorial with respect to…

We introduce a general version of singular compactness theorem which makes it possible to show that being a $\Sigma$-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed…

Several spectral sequence techniques are used in order to derive information about the structure of finite free resolutions of graded modules. These results cover estimates of the minimal number of generators of defining ideals of…

We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular…

For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and `real harmonic functions' with respect to A. We also consider certain groups…

In the computation of the intersection cohomology of Shimura varieties, or of the $L^2$ cohomology of equal rank locally symmetric spaces, combinatorial identities involving averaged discrete series characters of real reductive groups play…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

We describe (in a representation theoretic setting) a simple comparison of trace formulas, which implies that the conjugate of a Hilbert modular form $f$ by an automorphism of ${\Bbb C}$ again is a Hilbert modular form of the same level and…

We give an algebraic characterization of the syntax and semantics of a class of languages with variable binding. We introduce a notion of 2-signature: such a signature specifies not only the terms of a language, but also reduction rules on…