Related papers: Refining the Abel--Jacobi maps

A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic…

We relate the torsion part of the Abel-Jacobi kernel in the Griffiths group of 1-cycles to a birational invariant analogous to the degree 4 unramified cohomology and an invariant associated to the generalized Hodge conjecture in degree…

We study in this article the cohomological properties of Lagrangian families on projective hyper-K\"ahler manifolds. First, we give a criterion for the vanishing of Abel-Jacobi maps of Lagrangian families. Using this criterion, we show that…

This article investigates the Hodge theory of the moduli space of genus $g$ curves with $n$ marked points, establishing new connections between Schur-Weyl duality for $\mathfrak{sp}_{g}$ and higher Abel-Jacobi invariants. We develop a…

Let $X$ be a smooth projective curve over a field $k$ with an action of a finite group $G$. A well-known result of Chevalley and Weil describes the $k[G]$-module structure of cohomologies of $X$ in the case when the characteristic of $k$…

Let $X$ be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of $X$ in terms of the Hodge completed derived de Rham complex of $X$. In particular this…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

We construct classes in the motivic cohomology of certain 1-parameter families of Calabi-Yau hypersurfaces in toric Fano n-folds, with applications to local mirror symmetry (growth of genus 0 instanton numbers) and inhomogeneous…

In this paper, we will show that for a smooth quasi-projective variety over $\C,$ and a regular function $W:X\to \C,$ the periodic cyclic homology of the DG category of matrix factorizations $MF(X,W)$ is identified (unde Riemann-Hilbert…

We show that the image of the Abel-Jacobi map admits functorially a model over the field of definition, with the property that the Abel-Jacobi map is equivariant with respect to this model. The cohomology of this abelian variety over the…

In very rough terms, the main theorem is that the set, which consists of semistable vector bundles with trivial rational Chern classes and nontrivial kth cohomology on a smooth complex projective variety, is a degeneration of a union of…

This paper studies the Chow and cohomology rings of the Hacking moduli stack $\mathcal{P}^{\mathrm{H}}$ of plane quartics. We construct a smooth proper Deligne--Mumford stack resolving the Calabi--Yau wall crossing between the KSBA and…

For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant…

We show how to attach to any rigid analytic variety $V$ over a perfectoid space $P$ a rigid analytic motive over the Fargues-Fontaine curve $\mathcal{X}(P)$ functorially in $V$ and $P$. We combine this construction with the overconvergent…

We prove a restriction isomorphism for Chow groups of zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore, we study torsion subgroups of these groups…

We study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. We construct an inhomogeneous Picard-Fuchs equation by applying a Picard-Fuchs operator to the…

For the case of algebraic curves - compact Riemann surfaces - it is shown that de Rham cohomology group $H^{1}_{\mathrm{dR}}(X,\mathbb{C})$ of a genus $g$ Riemann surface $X$ has a natural structure of a symplectic vector space. Every…

We construct a functorial pushforward homomorphism in geometric Hodge filtered complex cobordism along proper holomorphic maps between arbitrary complex manifolds. This significantly improves previous results on such transfer maps and is a…

The goal of this article is to try understand where Hodge cycles on a singular complex projective variety X come from. As a first step we consider Hodge cycles on the maximal pure quotient $H^{2p}(X)/W_{2p-1}$, and introduce a class of…

Let $k$ be an algebraic field extension of $\mathbb{Q}$ and let $X$ be a smooth projective variety over $k$ of dimension $d \geq 2$. We study the pro-representability of the Chow group $CH^{p}(X)$ with $2 \leq p \leq d$. When certain Hodge…