相关论文: Additive Chow groups of schemes

We investigate Chow stability of projective bundles P(E) where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarisations L, the pair (P(E),L) is Chow stable and…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular…

Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain noncompact $3-$folds, called building blocks, satisfying a stability condition `at infinity'. Such bundles are known to…

We begin a study of the intersection theory of the moduli spaces of degree two stable maps from two-pointed rational curves to arbitrary-dimensional projective space. First we compute the Betti numbers of these spaces using Serre polynomial…

Rost defined the Chow group of algebraic cycles with coefficients in a locally constant torsion etale sheaf. We generalize the definition to allow non-torsion coefficients. Chow groups with twisted coefficients are related to Serre's notion…

A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a…

Given a separated scheme $X$ of finite type over a finite field, its higher Chow groups $CH_{-1}(X, 1)$ and $CH_{-2}(X, 3)$ are computed explicitly.

While higher bundles are of clear relevance to higher gauge theory, examples other than abelian bundle gerbes are hard to come across. One would in particular like to see 2-bundles where the structure 2-group is the String 2-group…

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…

In this paper, we investigate Murre's conjecture on the existence of a Chow--Kuenneth decomposition for a rational homogeneous bundle $Z\to S$ over a smooth variety, defined over complex numbers. Chow-K\"unneth decomposition is exhibited…

Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution…

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

We construct a moduli scheme $F[n]$ that parametrizes tuples $(S_1, S_2, \dots, S_{n+1}, p_1, p_2, \dots, p_n)$ in which $S_1$ is a fixed smooth surface over $\text{Spec } R$ and $S_{i+1}$ is the blowup of $S_i$ at a point $p_i$, $\forall…

We introduce a new ascending filtration, that we call the co-radical filtration in analogy with the basic theory of co-algebras, on the Chow groups of pointed smooth projective varieties. In the case of zero-cycles on projective…

If $X\subset\operatorname{Gr}(2,6)$ is the Fano variety of lines of a smooth cubic fourfold, then we show that the restriction to $X$ of any Schur functor of the tautological quotient bundle is modular and slope polystable. Moreover it is…

Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we construct smooth affine algebras $B$ over ${\mathbb F}_0$, with $\dim B=p+2$. Further, we construct…

The notion of modulus is a striking feature of Rosenlicht-Serre's theory of generalized Jacobian varieties of curves. It was carried over to algebraic cycles on general varieties by Bloch-Esnault, Park, R\"ulling, Krishna-Levine. Recently,…

Our investigation focuses on an additive analogue of the Bloch-Gabber-Kato theorem which establishes a relation between the Milnor $K$-group of a field of positive characteristic and a Galois cohomology group of the field. Extending the…