相关论文: Homological algebra in bivariant K-theory and othe…

We leverage the results of the prequel in combination with a theorem of D. Orlov to yield some results in Hodge theory of derived categories of factorizations and derived categories of coherent sheaves on varieties. In particular, we…

We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy…

Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented…

In this paper homological ideals associated to some Nakayama algebras are characterized and enumerated via integer specializations of some suitable Brauer configuration algebras. Besides, it is shown how the number of such homological…

The equivariant coarse Baum-Connes conjecture interpolates between the Baum-Connes conjecture for a discrete group and the coarse Baum-Connes conjecture for a proper metric space. In this paper, we study this conjecture under certain…

We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…

An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying…

In this paper, we provide new discrete uniformization theorems for bounded, $m$-connected planar domains. To this end, we consider a planar, bounded, $m$-connected domain $\Omega$ and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$…

In this article we describe the triangulated structure of the bounded derived category of a gentle algebra by describing the triangles induced by the morphisms between indecomposable objects in a basis of their Hom-space.

We show that the category of free rational G-spectra for a connected compact Lie group G is Quillen equivalent to the category of torsion differential graded modules over the polynomial cohomology ring on the classifying space, H*(BG). The…

In a previous paper, the author compute the dimension of Hochschild cohomology groups of Jacobian algebras from (unpunctured) triangulated surfaces, and gave a geometric interpretation of those numbers in terms of the number of internal…

In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in…

We exhibit the proximity frames and proximity homomorphisms as a Kleisli category of a comonad whose underlying functor takes a proximity frame to its frame of round ideals. This construction is known in the literature as {\em stable…

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.…

In this paper, we define and study (co)homology theories of a compatible associative algebra $A$. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define…

We develop a finite KKG-theory of C*-algebras following Arlettaz- H.Inassaridze's approach to finite algebraic K-theory. The Browder- Karoubi-Lambre's theorem on the orders of the elements for finite algebraic K-theory is extended to finite…

In this thesis we develop the cohomology of diagrams of algebras and then apply this to the cases of the $\lambda$-rings and the $\Psi$-rings. A diagram of algebras is a functor from a small category to some category of algebras. For an…

The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any…