Related papers: Rational analytic syntomic cohomology
In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded…
We give algorithms for the computation of the algebraic de Rham cohomology of open and closed algebraic sets inside projective space or other smooth complex toric varieties. The methods, which are based on Gr\"obner basis computations in…
In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded…
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…
As in our previous work [1] we address the problem to determine the splitting of the normal bundle of rational curves. With apolarity theory we are able to characterize some particular subvarieties in some Hilbert scheme of rational curves,…
Inspired by Bhatt-Scholze, we introduce prismatic cohomology for rigid analytic spaces with l.c.i singularities, with coefficients over Fontaine's de Rham period ring.
Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a subanalytic subset of $X$. We show that $X$ has a unique subanalytic triangulation compatible with the strata of $X$. We also show that every ${\rm C}^r$-orbifold, $1\leq…
We study the rational homology of the Deligne--Mumford compactification $\overline{\mathcal M}_{g,n}$ of the moduli space of stable curves via a family of Morse functions, namely the $\text{sys}_T$ functions. Exploiting the geometric and…
We develop a theory of arithmetic characteristic classes of (fully decomposed) automorphic vector bundles equipped with an invariant hermitian metric. These characteristic classes have values in an arithmetic Chow ring constructed by means…
We give a new method for calculating the cohomology of the normal bundles over rational varieties which are smooth projections of Veronese embeddings. The method can be used also when the projections are not smooth, in this case it provides…
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…
We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes of the standard tautological rings). While these algebras…
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…
We define a noncommutative analogue of invariant de Rham cohomology. More precisely, for a triple $(A,\mathcal{H},M)$ consisting of a Hopf algebra $\mathcal{H}$, an $\mathcal{H}$-comodule algebra $A$, an $\mathcal{H}$-module $M$, and a…
Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…
We explore and extend the application of homological algebra to describe quantum entanglement, initiated in arXiv:1901.02011, focusing on the Hodge-theoretic structure of entanglement cohomology in finite-dimensional quantum systems. We…
In this note, we introduce and study the Cartier--Witt stack $\mathrm{WCart}_X$ attached to a $p$-adic formal scheme $X$ as well as some variants. In particular, we reinterpret the notion of prismatic crystals on $X$ and their cohomology in…
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…
We investigate the problem of Poincar\'e duality for $L^p$ differential forms on bounded subanalytic submanifolds of $\mathbb{R}^n$ (not necessarily compact). We show that, when $p$ is sufficiently close to $1$ then the $L^p$ cohomology of…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…