Related papers: The Abel-Jacobi map for higher Chow groups

Let $X=Spec{A}$ denote a regular affine scheme, over a field $k$, with $1/2\in k$ and $\dim X=d$. Let $P$ denote a projective $A$-module of rank $n\geq 2$. Let $\pi_0\left({\mathcal LO}(P)\right)$ denote the (Nori) Homotopy Obstruction set,…

We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This result provides a unified way to understand known formulae for various geometric…

This paper forms the major portion of a talk given at the International Colloquium on Arithmetic, Algebra and Geometry at TIFR, Mumbai in Jan 2000. We look at the problem of detecting cycles with trivial Abel-Jacobi invariant. M. Green…

We study the affine ring of the affine Jacobi variety of a hyper-elliptic curve. The matrix construction of the affine hyper-elliptic Jacobi varieties due to Mumford is used to calculate the character of the affine ring. By decomposing the…

We study the arithmetic of abelian varieties over $K=k(t)$ where $k$ is an arbitrary field. The main result relates Mordell-Weil groups of certain Jacobians over $K$ to homomorphisms of other Jacobians over $k$. Our methods also yield…

The cosimplicial scheme $$Delta^bullet = \Delta^0 smallmatrix \to smallmatrix \Delta^1 smallmatrix to smallmatrix ...;\quad \Delta^n :=\Spec\Big(k[t_0,...c,t_n]/(\sum t_i -t)\Big)$$ was used in B to define higher Chow groups. In this note,…

It is shown that the middle quasi-homomorphisms of Fujiwara and Kapovich are precisely constant perturbations of quasi-homomorphisms. Quasi-polynomial maps are defined and their constructibility is explored. In particular, it is shown that…

We prove Bloch's formula for the Chow group of 0-cycles with modulus on smooth projective varieties over finite fields. The proof relies on two new results in global ramification theory.

On \'etudie les cycles alg\'ebriques de codimension 3 sur les hypersurfaces cubiques lisses de dimension 5. Pour une telle hypersurface, on d\'emontre d'une part que son groupe de Griffiths des cycles de codimension 3 est trivial et d'autre…

This paper proposes a conjectural picture for the structure of the Chow ring of a (projective) hyper-K\"ahler variety, and the construction of a Beauville decomposition, with emphasis on the Chow group of $0$-cycles, which is endowed with a…

We relate Fourier transforms between compactified Jacobians over the moduli space of stable curves to logarithmic Abel-Jacobi theory. As an application, we compute the pushforward of divisor monomials on compactified Jacobians in terms of…

We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new…

To a compact tropical variety of arbitrary dimension, we associate a collection of intermediate Jacobians defined in terms of tropical homology and tropical monodromy. We then develop an Abel-Jacobi theory in the tropical setting by…

We describe the geometrical ladder of equations for Abelian bundles and gerbes, as well as higher generalisations, in terms of the cohomology of an operator that combines de Rham and Cech cohomology.

Let $G$ be a connected reductive group, and $G/B$ be its flag variety. Let $\pi:G\to G/B$ be the natural projection. In this paper, we developed an algorithm to describe the map $\pi^* :\operatorname{CH}^*(G/B;\mathbb{F}_p)\longrightarrow…

We construct a variant of Karoubi's relative Chern character for smooth, separated schemes over the ring of integers in a p-adic field and prove a comparison with the rigid syntomic regulator. For smooth projective schemes we further relate…

In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We…

Extending a result of Schr\"oer on a Grothendieck question in the context of complex analytic spaces, we prove that the surjectivity of the Brauer map $\delta: Br(X) \rightarrow H_{\rm \'et}^2(X,\mathbb{G}_{m, X})_{\rm tor}$ for algebraic…

We prove several results about integral versions of Fourier duality for abelian schemes, making use of Pappas's work on integral Grothendieck-Riemann-Roch. If $S$ is smooth quasi-projective of dimension $d$ over a field and $\pi \colon X\to…

We consider a simple modification of the Chow group CH^2(Spec(k),3) using only linear subvarieties in affine spaces and show that it maps surjectively to the Bloch group B(k) for any infinite field k. We also describe the kernel of this…