Related papers: Mixed Hodge structures and formality
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Assuming the K\"unneth type standard conjecture, we propose a way to describe objects of mixed motives explicitly. We study their formal properties, and we associate mixed motives to schemes smooth and separated over a field. This serves as…
We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.
We propose a definition of ``nonabelian mixed Hodge structure'' together with a construction associating to a smooth projective variety $X$ and to a nonabelian mixed Hodge structure $V$, the ``nonabelian cohomology of $X$ with coefficients…
This text is an expository survey on the interplay between polarized variation of Hodge structure (PVHS) and the formalism of Hodge modules. We specifically review the extensions of a PVMHS over their singularities and its relation to mixed…
The aim of this article is to study degeneration of the variations of Hodge structure associated to a proper K\"ahler semistable morphism. We prove that the weight filtrations constructed in the author's previous paper coincide with the…
We describe locally the representation varieties of fundamental groups for smooth complex varieties at representations coming from the monodromy of a variation of mixed Hodge structure. Given such a manifold $X$ and such a linear…
We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.
''Positive geometries'' are a class of semi-algebraic domains which admit a unique ''canonical form'': a logarithmic form whose residues match the boundary structure of the domain. The study of such geometries is motivated by recent…
The purpose of this article is to investigate the properties of the category of mixed plectic Hodge structures defined by Nekov\'a\v{r} and Scholl. We give an equivalent description of mixed plectic Hodge structures in terms of the weight…
We show that, for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal…
Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.
We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is…
We prove the formality theorem for the differential graded Lie algebra module of Hochschild chains for the algebra of endomorphisms of a smooth vector bundle. We discuss a possible application of this result to a version of the algebraic…
We study a geometric notion related to formality for Bott-Chern cohomology on complex manifolds.
We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…
We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties…
In this paper, we define a certain Hodge-theoretic structure for an arbitrary variety X over the complex number field by using the theory of mixed Hodge module due to Morihiko Saito. We call it an arithmetic Hodge structure of X. It is…
We give a complex polarized variation of Hodge structure over a compact K"ahler manifold $M$ which controls all finite-dimensional complex polarized variations of Hodge structure over $M$ and their tensor relations. As a corollary, we…
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…