Related papers: K-Theory for Triangulated Categories III(A): The T…

We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action…

We construct and study a candidate for the standard motivic t-structure on the triangulated category of relative cohomological 1-motives with rational coefficients over a noetherian finite dimensional scheme S. This t-structure is defined…

We define the notion of right $n$-angulated category, which generalizes the notion of right triangulated category. Let $\mathcal{C}$ be an additive category or $n$-angulated category and $\mathcal{X}$ a covariantly finite subcategory, we…

We give a characterisation of those local not necessary commutative rings, for which the category of projective modules admits a triangulation with the identity as translation functor. By "admits a triangulation" we mean that the category…

Motivated by the splitting principle, we define certain simplicial complexes associated to an associative ring $A$, which have an action of the general linear group $GL(A)$. This leads to an exact sequence, involving Quillen's algebraic…

A simple graph is called triangular if every edge of it belongs to a triangle. We conjecture that any graphical degree sequence all terms of which are greater than or equal to 4 has a triangular realisation, and establish this conjecture…

In the present paper we propose a geometric model of the twisted K-theory corresponding to elements of finite order in $H^3(X, \mathbb{Z})\times [X, \BBSU_\otimes]$.

In this paper, we apply quantitative operator K-theory to develop an algorithm for computing K-theory for the class of filtered C *-algebras with asymptotic finite nuclear decomposition. As a consequence, we prove the K{\"u}nneth formula…

In this paper we give a different proof of Quillen's D\'evissage theorem using Barwick's theorem of the heart. The key ingredient is a certain short exact sequence of dg categories, which is closely related with the Auslander-type…

Consider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beilinson, Bernstein and Deligne consider in this setting a…

We introduce the notion of asymptotic Grothendieck groups for abelian and triangulated categories that are both AB4 and AB4*. We study when the asymptotic Grothendieck group of the heart of a triangulated category with a t-structure is…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…

Let $\mathcal{A}$ be an abelian category with a torsion pair $(\mathcal{T},\mathcal{F})$. Happel-Reiten-Smalo tilting provides a method to construct a new abelian category $\mathcal{B}$ with a torsion pair associated to…

We prove that given any strong, stable derivator and a $t$-structure on its base triangulated category $\cal D$, the $t$-structure canonically lifts to all the (coherent) diagram categories and each incoherent diagram in the heart uniquely…

In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context.…

This thesis deals with the general problem of determining when the heart $\mathcal{H}$ of a t-structure in a triangulated category $\mathcal{D}$ is a Grothendieck or a module category. As preliminaries, we study Grothendieck conditions…

Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists…

We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…

We consider the effect of $t$-structures on the Tannaka duality theory for dg categories developed in our previous paper. We associate non-negative dg coalgebras $C$ to dg functors on the hearts of $t$-structures, and relate dg…