Related papers: Chow groups of one-dimensional noetherian domains

We produce an infinite family of imaginary quadratic fields whose ideal class groups have $3$-rank at least $2$.

Let X be a smooth compactification of a connected linear algebraic group over a field k. The Chow group of degree nought zero-cycles on X is a torsion group. When k is a p-adic field, we show that the prime-to-p component of this group is…

We determine the set of catenary degrees, the set of distances, and the unions of sets of lengths of the monoid of nonzero ideals and of the monoid of invertible ideals of orders in quadratic number fields.

We compute the spinor class field for a genus of orders, in a central simple algebra of higher dimension, that are intersections of two maximal orders. In particular, we compute the number of spinor genera in a genus of such orders, as the…

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…

We show an example of Chow group of 0-cycles on surface over a p-adic field which has infinite torsion subgroup.

We define tautological Chow classes on the moduli space of curves with linear series. In the case where the forgetful morphism to the moduli space of curves has relative dimension zero, we describe the images of these classes in the Chow…

The focus of this note is on the Chow group problem over ramified regular local rings $(R, m)$. Our goal is threefold: i) to introduce a characterization of a ramified regular local ring essentially of finite type over a dvr, ii) to address…

We give bounds on the order of torsion in the Chow group of zero dimensional cycles for isotropic Grassmannians and Brauer-Severi flag varieties. To do this, we introduce tools to understand the behavior of torsion in Chow groups with…

We construct a family of ideals representing ideal classes of order 2 in quadratic number fields and show that relations between their ideal classes are governed by certain cyclic quartic extensions of the rationals.

An earlier wrong formula for the dimension of the first Chow group of a Hilbert scheme of space curves is corrected.

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

We study the freeness of the group $\mathrm{Inv}(D)$ of invertible ideals of an integral domain $D$, and the freeness of some related groups of (fractional) ideals. We study the relation between $\mathrm{Inv}(D)$ and $\mathrm{Inv}(D_P)$, in…

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…

We prove that a smooth proper universally CH_0-trivial variety X over a field k has universally trivial Brauer group. This fills a gap in the literature concerning the p-torsion of the Brauer group when k has characteristic p.

Let X be a complex smooth affine irreducible curve, and let D = D(X) be the ring of global differential operators on X. In this paper, we give a geometric classification of left ideals in $ D $ and study the natural action of the Picard…

We introduce a generalisation of norm relations in the group algebra Q[G], where G is a finite group. We give some properties of these relations, and use them to obtain relations between the S-unit groups of different subfields of the same…

For each finite subgroup $G$ of $PGL_2(\mathbb{Q})$, and for each integer $n$ coprime to $6$, we construct explicitly infinitely many Galois extensions of $\mathbb{Q}$ with group $G$ and whose ideal class group has $n$-rank at least…

Let $k$ be a field of arbitrary characteristic. Let $S$ be a singular surface defined over $k$ with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation $\tilde{S}$ is finite dimensional.…

We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.