Related papers: Derived Manifolds as Differential Graded Manifolds

We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the product of a torus with a finite volume hyperbolic…

Let G be a finite group. The unit sphere in a finite-dimensional orthogonal G-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue, and establish its basic properties…

We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal approaches within a unifying framework. First, we establish a…

Using standard analysis only, we present an extension ${^\bullet\R}$ of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential…

We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable…

We show that for the path algebra $A$ of an acyclic quiver, the singularity category of the derived category $\mathsf{D}^{\rm b}(\mathsf{mod}\,A)$ is triangle equivalent to the derived category of the functor category of…

We prove in this paper that for a quasi-compact and semi-separated (non necessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of Hovey, Palmieri and…

We prove that groups that are mod-p-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings' 1963 result for the lower-central p-series. Similarly spaces that are mod-p-homology…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

This paper surveys the recent advances concerning the relations between triangulated (or derived) categories and their dg enhancements. We explain when some interesting triangulated categories arising in algebraic geometry have a unique dg…

We construct rational models for classifying spaces of self-equivalences of bundles over simply connected finite CW-complexes relative to a given simply connected subcomplex. Via work of Berglund-Madsen and Krannich this specializes to…

An unrepresentable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical…

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of…

We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, also a complete stable equivalence classification of…

In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show that the totalization agrees with the homotopy limit in the…

Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…