Related papers: Chern subrings

Using similarities between topological $K$-theory and periodic cyclic homology we show that, after tensoring with $\mathbb C$, for certain Fr\'echet algebras the Chern character provides an isomorphism between these functors. This is…

We prove that Chern classes in continuous $\ell$-adic cohomology of automorphic bundles associated to representations of $G$ on a projective Shimura variety with data $(G,X)$ are trivial rationally. It is a consequence of Beilinson's…

A theorem of Batyrev's asserts that if two nonsingular varieties V,W are birational, and their canonical bundles agree after pull-back to a resolution of indeterminacies of a birational map between them, then the Betti numbers of V and W…

This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative…

Let $\mathfrak{g}$ be a simple Lie algebra of exceptional type over an algebraically closed field $k$, and let $G$ be a simple linear algebraic group with Lie algebra $\mathfrak{g}$. For $\mathrm{char} \, k =p >0$, we present a complete…

We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split groups done by Kac to the non-split quasi-split case. For the…

The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally…

We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section…

We describe the equivariant Chow ring of the wonderful compactification $X$ of a symmetric space of minimal rank, via restriction to the associated toric variety $Y$. Also, we show that the restrictions to $Y$ of the tangent bundle $T_X$…

This small note is about Pl\"ucker hyperplane sections $X$ of the Grassmannian $\operatorname{Gr}(3,V_{10})$. Inspired by the analogy with cubic fourfolds, we prove that the only non-trivial Chow group of $X$ is generated by Grassmannians…

We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the ``Weyl…

We compute the Chern subgroup of the 4-th integral cohomology group of a certain classifying space and show that it is a proper subgroup. Such a classifying space gives us new counterexamples for the integral Hodge and Tate conjectures…

Let G be a complex connected reductive group. The representation ring R(G) admits a canonical filtration defined in terms of the lambda-structure. We compute the associated graded ring gr R(G) (over Q) and the Chern classes of a…

An odd index theorem for higher odd Chern characters of crossed product algebras is proved. It generalizes the Noether-Gohberg-Krein index theorem. Furthermore, a local formula for the associated cyclic cocycle is provided. When applied to…

Suppose $X$ is a smooth complex algebraic variety. A necessary condition for a complex topological vector bundle on $X$ (viewed as a complex manifold) to be algebraic is that all Chern classes must be algebraic cohomology classes, i.e., lie…

We provide an alternative proof that the Chow group of $1$-cycles on a Severi--Brauer variety associated to a biquaternion division algebra is torsion-free. There are three proofs of this result in the literature, all of which are due to…

We compute the Chow ring of the classifying space $BSO(2n,\C)$ in the sense of Totaro using the fibration $Gl(2n)/SO(2n) \to BSO(2n) \to BGl(2n)$ and a computation of the Chow ring of $Gl(2n)/SO(2n)$ in a previous paper. We find this Chow…

A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety which have almost all the properties of the…

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology for compact quantum groups, define Chern characters between them and show that the Chern characters in both topological and algebraic…

We give an example of an algebraic torus $T$ such that the group $\operatorname{CH}^2(BT)_{\operatorname{tors}}$ is non-trivial. This answers a question of Blinstein and Merkurjev.