Related papers: $q$-de Rham complexes of higher level

Many coupled problems in engineering and science can be described by elliptic partial differential equations on adjacent domains, where the coupling can be considered either as a thin equidimensional overlap between the model domains, or as…

Over the complex numbers, the complement of a collection of hyperplanes is a widely-studied object; the cohomology ring, in particular, is known to have a structure depending only on the combinatorial properties of the intersection of…

In this article, we analyze the connection between the Log De Rham Cohomology of an fs (not necessary log smooth) log scheme $Y$ over $\mathbb C$ (for $Y$ admitting an exact closed immersion into an fs log smooth log scheme over $\mathbb…

We study the homology of the dual de Rham complex as functors on the category of abelian groups. We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the…

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie…

We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions of the de Rham complex of differential forms built on…

We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applications of our result, we deduce Drinfeld's refinement of the…

We construct the crystalline fundamental group of a semi-stable variety over a field of positive characteristic using the log De Rham-Witt complex and Navarro-Aznar's derived Thom-Whitney functor. This approach gives a relatively direct…

We consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the…

In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by…

The study of differential forms that are closed but not exact reveals important information about the global topology of a manifold, encoded in the de Rham cohomology groups $H^k(M)$, named after Georges de Rham (1903-1990). This expository…

In this article we give an interpretation, in terms of derived de Rham complexes, of Scholze's de Rham period sheaf and Tan--Tong's crystalline period sheaf.

We show that the sum of the local cohomological dimension and the rectified $\mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological…

Using methods of homological algebra, we obtain an explicit crystal isomorphism between two realizations of crystal bases of the lower part of the quantized enveloping algebra of (almost all) finite dimensional simply-laced Lie algebras.…

We construct a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of logarithmic algebraic geometry and is remarkable…

This paper studies the derived de Rham cohomology of F_p and p-adic schemes, and is inspired by Beilinson's recent work. Generalising work of Illusie, we construct a natural isomorphism between derived de Rham cohomology and crystalline…

Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme over $\Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholze's prismatic site $(X/A)_{\prism}$ of $X$ relative to $A$. We prove that if $X$ is proper over…

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of…

Let $Y/S$ be a $p$-completely smooth morphism of $p$-torsion free $p$-adic formal schemes endowed with a Frobenius lift, and let $\overline Y/\overline S$ denote its reduction modulo $p$. We show that the category of crystals on the…

We show the coherence of the direct images of the De Rham complex relative to a flat holomorphic map with suitable boundary conditions. For this purpose, a notion of bi-dg-algbera called the Koszul-De Rham algbera is dveloped.