Cyclic homology and de Rham cohomology.
De Rham cohomology and homotopy Frobenius manifolds
We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.
Décomposition de la cohomologie cyclique bivariante des algèbres commutatives.
Decompositions of the category of noncommutative sets and Hochschild and cyclic homology
In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.
Deformations and derived categories
In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...
Deformations of (bi)tensor categories
Derivations of categorical groups.
Derivations of crossed modules.
Derivations of homotopy algebras
We recall the definition of strong homotopy derivations of algebras and introduce the corresponding definition for algebras. We define strong homotopy inner derivations for both algebras and exhibit explicit examples of both.
Derivations, semidirect products and reduced cyclic cohomology.
Derived de Rham Complex and Cyclic Homology.
Derived functors of and abelian ab3*- and Ab4*-categories with enough injectives
Diffeotopy functors of ind-algebras and local cyclic cohomology.
Differential equations, Spencer cohomology, and computing resolutions.
Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
Directed homotopy theory, I
Directed homotopy theory, II. Homotopy constructs.
Distributive laws and Koszulness
Distributive law is a way to compose two algebraic structures, say and , into a more complex algebraic structure . The aim of this paper is to understand distributive laws in terms of operads. The central result says that if the operads corresponding respectively to and are Koszul, then the operad corresponding to is Koszul as well. An application to the cohomology of configuration spaces is given.
Double complexes and vanishing of Novikov cohomology
2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that...
Dualité dans la catégorie des complexes filtrés d'opérateurs differentiels d'ordre ≤ 1.
Let X be a separated scheme of finite type on a field k, the characteristic of k being assumed not equal to 2. We construct a duality for complexes of sheaves of Ox modules with maps differential operators of order ≤ 1. This theory is an extension of the theory built by R. Hartshorne for complexes with linear maps.