Related papers: The Hodge theoretic fundamental group and its coho…

Hodge theory associates to a smooth projective variety over $\mathbb{C}$ a piece of linear algebra information, called a $\mathbb{Q}$-Hodge structure. Conversely, it is a natural question which abstract $\mathbb{Q}$-Hodge structures arise…

The aim of this paper is to study the behavior of Hodge-theoretic (intersection homology) genera and their associated characteristic classes under proper morphisms of complex algebraic varieties. We obtain formulae that relate (parametrized…

We study partial homology and cohomology from ring theoretic point of view via the partial group algebra $\mathbb{K}_{par}G$. In particular, we link the partial homology and cohomology of a group $G$ with coefficients in an irreducible…

This paper studies the possible Hodge groups of simple polarizable $\mathbb{Q}$-Hodge structures with Hodge numbers $(n,0,\ldots,0,n)$. In particular, it generalizes earlier work of Ribet and Moonen-Zarhin to completely determine the…

We show that the usual Hodge conjecture implies the general Hodge conjecture for certain abelian varieties of type III, and use this to deduce the general Hodge conjecture for all powers of certain 4-dimensional abelian varieties of type…

Let $X$ be a complex algebraic variety. With $\mathbb{Q}$-coefficients, the compactly supported cohomology groups $H^{i}_{c}(X, \mathbb{Q})$ and the compactly supported intersection cohomology groups $IH^{i}_{c}(X, \mathbb{Q})$ have mixed…

We extend the notion of a partial cohomology group $H^n(G,A)$ to the case of non-unital $A$ and find interpretations of $H^1(G,A)$ and $H^2(G,A)$ in the theory of extensions of semilattices of abelian groups by groups.

Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the…

This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$…

We show that if X is any proper complex variety, there is a weight decomposition on the real schematic homotopy type, in the form of an algebraic G_m-action. This extends to a real Hodge structure, in the form of a discrete C^*-action, such…

On a smooth algebraic curve X with genus greater than 1 we consider a flat principal bundle with a reductive structure group S and a vector bundle associated with it. To this set of information we put in correspondence a pro-algebraic group…

We prove two results regarding Hodge structures appearing in the cohomology of complex tori. First, we prove that if a polarizable Hodge structure appears in the cohomology of a complex torus $T$, it appears in the cohomology of an abelian…

We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of…

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…

A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…

We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair, consisting of a group-like element and a character, in involution. This provides the key construct allowing to extend cyclic cohomology to Hopf…

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural…

We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure, a notion introduced in [GNPR10] leading to a good calculation of the homotopy category in terms of (co)fibrant objects. This result provides a…