Related papers: K-theory and 0-cycles on schemes

We prove an Artin-Rees type theorem for algebraic cycles and give an application to zero cycles.

In this note we show that given a smooth affine variety $X$ over an algebraically closed field $k$ and an effective (possibly non reduced) Cartier divisor $D$ on it, the Kerz-Saito Chow group of zero cycles with modulus ${\rm CH}_0(X|D)$ is…

Let $X$ be a hyperk\"ahler variety, and assume $X$ has a non-symplectic automorphism $\sigma$ of order $>{1\over 2}\dim X$. Bloch's conjecture predicts that the quotient $X/<\sigma>$ should have trivial Chow group of $0$-cycles. We verify…

We show how the notion of the transcendence degree of a zero-cycle on a smooth projective variety X is related to the structure of the motive M(X). This can be of particular interest in the context of Bloch's conjecture, especially for…

In this paper, the generalized Bloch Conjecture on zero cycles for the quotient of certain complete intersections with trivial canonical bundle is proved to hold. As an application of Bloch-Srinivas method on the decomposition of the…

A good way of parametrizing 0-dimensional schemes in an affine space $\mathbb{A}_K^n$ has been developed in the last 20 years using border basis schemes. Given a multiplicity $\mu$, they provide an open covering of the Hilbert scheme ${\rm…

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of…

For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, the zero loci of those…

In this paper we prove a finiteness result concerning the Chow group of zero-cycles for varieties over $p$-adic local fields. In this final version, there are several corrections concerning mathematical symbols and reference to related…

We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting the basic ribbon product rule in NSym via concatenation and…

We define a filtration on the Chow groups of a smooth projective variety X over a field k by using the cycle map into continuous l-adic etale cohomology. The main theorem says that if k is a function field in one variable over a finite…

We construct level-0 modules of the quantum affine algebra $\Uq$, as the $q$-deformed version of the Lie algebra loop module construction. We give necessary and sufficient conditions for the modules to be irreducible. We construct the…

Let $X$ be a hyperk\"ahler variety, and assume that $X$ admits a non-symplectic automorphism $\sigma$ of order $k>{1\over 2}\dim X$. Bloch's conjecture predicts that the quotient $X/<\sigma>$ should have trivial Chow group of $0$-cycles. We…

In this paper we study the group $A_0(X)$ of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety $X$. To do this we translate rational equivalence of 0-cycles on a projective variety…

The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by \v{C}ech cohomology of the tiling space) and the spectral properties (of Hamiltonians…

The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…

We show that the higher Chow groups with modulus of Binda-Kerz-Saito for a smooth quasi-projective scheme $X$ is a module over the Chow ring of $X$. From this, we deduce certain pull-backs, the projective bundle formula, and the blow-up…

We prove a colimit formula for the K-theory spectra of reductive p-adic groups of rank one with regular coefficients in terms of the K-theory of certain compact open subgroups. Furthermore, in the complex case, we show, using the…

We prove a result about the non-existence of certain sums-of-squares formulas over a field. This generalizes an old theorem which used topological K-theory to obtain obstruction conditions when the field is the real numbers. Our result…

In this paper, we define the $K$-theoretic Hall algebra for $0$-dimensional coherent sheaves on a smooth projective surface, prove that the algebra is associative and construct a homomorphism to a redefined shuffle algebra analogous to…