Related papers: The Chow rings of $G_2$ and $Spin_7$

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1$ branched over $n+2$ points. We prove that for a very…

B. Schuster \cite{SCH1} proved that the $mod$ 2 Morava $K$-theory $K(s)^*(BG)$ is evenly generated for all groups $G$ of order 32. For the four groups $G$ with the numbers 38, 39, 40 and 41 in the Hall-Senior list \cite{H}, the ring…

Schur rings are a type of subring of the group ring that is spanned by a partition of the group that meets certain conditions. Past literature has exclusively focused on the finite group case. This paper extends many classic results about…

We compute Chow groups of moduli spaces of rank 2 vector bundles on curves with determinant of odd degree in terms of generators and relations.

A local-global sequence for Chow groups of zero-cycles involving Brauer groups has been conjectured to be exact for all proper smooth algebraic varieties. We apply existing methods to construct several new families of varieties verifying…

One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous…

Let $K$ be a field of characteristic zero and let $Sm/K$ be the category of smooth and separated schemes over $K$. For an ind-scheme $\mathcal X$ (and more generally for any presheaf of sets on $Sm/K$), we define its Chow groups…

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…

We give an explicit description of $\overline{\mathcal{M}}_{1,2}$ as a weighted blow-up of a weighted projective stack. We use this description to compute the Brauer group of $\overline{\mathcal{M}}_{1,2;S}$ over any base scheme $S$ where 6…

The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^{d-g}, whose full details will appear in a subsequent paper. In particular, we extend the previous…

We describe a theory of logarithmic Chow rings and tautological subrings for logarithmically smooth algebraic stacks, via a generalisation of the notion of piecewise-polynomial functions. Using this machinery we prove that the double-double…

The integral equivariant Chow ring of S0(4) is computed via the geometry of ruled quadric surfaces in P^3.

We compute the versal deformation ring of a split generic $2$-dimensional representation $\chi_1\oplus \chi_2$ of the absolute Galois group of $\mathbb{Q}_p$. As an application, we show that the Breuil--M\'ezard conjecture for both…

We prove that certain Fano fourfolds of K3 type constructed by Fatighenti-Mongardi have a multiplicative Chow-K\"unneth decomposition. We present some consequences for the Chow ring of these fourfolds.

We prove a decomposition theorem for the cohomological Chow group of 0-cycles on the double of a quasi-projective $R_1$-scheme over a field along a closed subscheme, in terms of the Chow groups, with and without modulus, of the scheme. This…

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the…

We analyze finite orbits of the natural braid group action on the character variety of the $n$ times punctured sphere. Building on recent results relating middle convolution and finite complex reflection groups, our work implements Katz's…

A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible…

We determine that the Chow ring (with ${\bf Q}$-coefficients) of the Hurwitz space parametrizing degree three covers of ${\bf P}^{1}$ is tautological. We also compute the rational Picard groups of auxiliary spaces of degree three maps with…

We compute the Chow group of a Ch{\^a}telet surface over a dyadic field. Combined with the previous work of Bloch, Colliot-Th{\'e}l{\`e}ne, Coray, Ischebeck, Sansuc, Swinnerton-Dyer, and the author, this allows one to compute the Chow group…