Related papers: On the Chow ring of the classifying stack of PGL_3

We determine a subring of the Chow ring and the cohomology of $BPGL_n$, the classifying space of the projective linear group of degree $n$ over complex numbers, and explain a way in which this computation might play a role in the…

Let p be an odd prime. We show that for a simply-connected semisimple complex linear algebraic group, if its integral homology has p-torsion, the Chern classes do not generate the Chow ring of its classifying space.

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…

In the integral cohomology ring of the classifying space of the projective linear group $PGL_n$ (over $\mathbb{C}$), we find a collection of $p$-torsions $y_{p,k}$ of degree $2(p^{k+1}+1)$ for any odd prime divisor $p$ of $n$, and $k\geq…

Let $GO(2n)$ be the general orthogonal group scheme (the group of orthogonal similitudes). In the topological category, Y. Holla and N. Nitsure determined the singular cohomology ring $H^*_{\rm sing}(BGO(2n,\mathbb C),\mathbb F_2)$ of the…

We compute $CH^*BG_2$ and $CH^*BSpin_7$, using in particular the stratification method introduced by Vezzosi. We also give some information on the Chow rings of the finite groups $G_2(q)$. This new version includes an appendix, which will…

We investigate the integral cohomology ring and the Chow ring of the classifying space of the complex projective linear group PGL_p, when p is an odd prime. In particular, we determine its additive structure completely, and we reduce the…

We show how the stratification method, introduced by Vezzosi in his study of PGL_3, provides a unified approach to the known computations of the Chow rings of the classifying spaces of GL_n, SL_n, Sp_n, O_n and SO_n.

A result of A. King and C. Walter asserts that the Chow ring of a fine quiver moduli space is generated by the Chern classes of universal bundles if the quiver is acyclic. We will show that defining relations between these Chern classes…

Let X be a K3 surface. We show that the Chow group CH_0(X) of 0-cycles contains a "fundamental class" c_X of degree 1 with remarkable properties: any product of divisors is proportional to this class, and so is the second Chern class…

In this paper we calculate the ring of unstable (possibly non-additive) operations from algebraic Morava K-theory K(n) to Chow groups with $\mathbb{Z}_{(p)}$-coefficients. More precisely, we prove that it is a formal power series ring on…

We investigate the structure of the Chow ring of the classifying stacks $BT$ of algebraic tori, as it has been defined by B. Totaro. Some previous work of N. Karpenko, A. Merkurjev, S. Blinstein and F. Scavia has shed some light on the…

Using determinantal schemes, we construct explicit cycles in the higher Chow complex of BGL that represent the universal Chern classes in higher Chow groups. As an application, we use these cycles, along with a canonical \emph{stable moving…

We define the Chow ring of the classifying space of a linear algebraic group. In all the examples where we can compute it, such as the symmetric groups and the orthogonal groups, it is isomorphic to a natural quotient of the complex…

The projective linear group $\text{PGL}(3)$ naturally acts on the Grassmannian $\text{Gr}(3, V_2)$ of $3$-dimensional subspaces of the vector space $V_2$ of homogeneous conics in 3 variables. It was proved by Abdallah, Emsalem and Iarrobino…

This paper provides a computation of the mod 2 Chow ring of the motivic \'etale classifying space of the finite group $\mathrm{Syl}_2(\mathrm{GL}(4,2))$. It outlines a general computation strategy, adapted from work by Burt Totaro, that has…

The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of…

We study the Chow ring with rational coefficients of the moduli space $\mathcal F_{2}$ of quasi-polarized $K3$ surfaces of degree $2$. We find generators, relations, and calculate the Chow Betti numbers. The highest nonvanishing Chow group…

We compute the integral Chow ring of the quotient stack $[(\mathbb{P}^1)^n/PGL_2]$, which contains $\mathcal{M}_{0,n}$ as a dense open, and determine a natural $\mathbb{Z}$-basis for the Chow ring in terms of certain ordered incidence…

We compute the cobordism ring $MU^*(BG)\otimes \mathbb{F}_p$ when $G$ is a Chevalley group. In the particular case of the general linear group, we prove that it agrees with the Chow ring (as defined by Totaro).