Related papers: Deligne-Hodge-DeRham theory with coefficients

In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the \textit{schematization functor} $X \mapsto (X\otimes \mathbb{C})^{sch}$,…

We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…

We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that the 1-forms naturally define a lift of the variation of mixed…

On an $n$-dimensional locally reduced complex analytic space $X$ on which the shifted constant sheaf $\Q_X^\bullet[n]$ is perverse, it is well-known that, locally, $\Q_X^\bullet[n]$ underlies a mixed Hodge module of weight $\leq n$ on $X$,…

In the article of Hesselholt [Hes05], a set of conjectures is laid out. Given a smooth scheme $X$ over the ring of integers $\mathcal{O}_K$ of a $p$-adic field $K$, these conjectures concern the expected relation between log topological…

We associate to each algebraic variety defined over $\mathbb{R}$ a filtered cochain complex, which computes the cohomology with compact supports and $\mathbb{Z}\_2$-coefficients of the set of its real points. This filtered complex is…

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…

We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the…

In this paper, we prove the l-independence of monodromy weight filtration for a geometrically smooth variety over an equicharacteristic local field. We also prove the l-independence for the geometric monodromy representation on the…

For a smooth complex projective variety X defined over a number field, we have filtrations on the Chow groups depending of the choice of realizations. If the realization consists of mixed Hodge structure without any additional structure, we…

There are several interesting filtrations on the Cartan subalgebra of a complex simple Lie algebra coming from very different contexts: one is the principal filtration coming from the Langlands dual, one is coming from the Clifford algebra…

Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…

Let X be a smooth, projective variety over the field of complex numbers. On the space H of its rational cohomology of degree i we have the arithmetic filtration F^p. On the other hand, on the space of cohomology of degree i of X with…

We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise…

We give a $K$-theoretic and geometric interpretation for a generalized weighted Ehrhart theory of a full-dimensional lattice polytope $P$, depending on a given homogeneous polynomial function $\varphi$ on $P$, and with Laurent polynomial…

We introduce a category of possibly irregular holonomic D-modules which can be endowed in a canonical way with an irregular Hodge filtration. Mixed Hodge modules with their Hodge filtration naturally belong to this category, as well as…

We study the relation between the Hodge filtration of the de Rham cohomology of a proper smooth supervariety $X$ and the usual Hodge filtration of the corresponding reduced variety $X_0$.

For a smooth projective scheme $X$ over a ring $R$ on which $p$ is nilpotent that meets some general assumptions we prove that the crystalline cohomology is equipped with the structure of a higher display which is a relative version of…

We give a description of the cohomology groups of the structure sheaf on smooth compactifications $\overline{X}(w)$ of Deligne--Lusztig varieties $X(w)$ for ${\rm GL}_n$, for all elements $w$ in the Weyl group. As a consequence, we obtain…

There is a natural descending filtration on the singular cohomology of a complex smooth projective variety called the coniveau filtration. The generalized Hodge conjecture would imply, rather trivially, that the coniveau filtration is…