Related papers: Amitsur subgroup and noncommutative motives

We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent…

This article focuses on smooth, projective, and geometrically integral varieties $X$ defined over a number field $k$ with torsion-free geometric Picard groups. We establish an isomorphism between the Brauer groups of $X$ and its symmetric…

In the paper M. Somekawa, {\it{On Milnor $K$-groups attached at semi-Abelian varieties}}, K-theory, \textbf{4} (1990) p.105, Somekawa conjectures that his Milnor K-group $K(k,G_1,...,G_r)$ attached to semi-abelian varieties $G_1$,...,$G_r$…

Given a prime number $p$, we perform the study of Chow motives and motivic decompositions, with coefficients in $\mathbb{Z}/p\mathbb{Z}$, of projective homogeneous varieties for $p'$-inner $p$-consistent reductive algebraic groups. Assorted…

For an oriented cohomology theory A and a relative cellular space X, we decompose the A-motive of X into a direct sum of twisted motives of the base spaces. We also obtain respective decompositions of the A-cohomology of X. Applying them,…

Let $X_1$ and $X_2$ be deformation equivalent projective hyperk\"ahler manifolds. We prove that the Andr\'e motive of $X_1$ is abelian if and only if the Andr\'e motive of $X_2$ is abelian. Applying this to manifolds of $\mbox{K3}^{[n]}$,…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

A toric degeneration of an irreducible variety is a flat degeneration to an irreducible toric variety. In the case of a flag variety, its toric degeneration with desirable properties induces degenerations of Richardson varieties to unions…

We briefly report on our result that the braided tensor product algebra of two module algebras $A_1,A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $H_1$ with a subalgebra isomorphic to $A_2$…

In this article we further the study of non-commutative motives. Our main result is the construction of a symmetric monoidal structure on the localizing motivator Mot of dg categories. As an application, we obtain : (1) a computation of the…

We study a collection of Hessenberg varieties in the type A flag variety associated to a nonzero semisimple matrix whose conjugacy class has minimal dimension. We prove each such minimal semisimple Hessenberg variety is a union Richardson…

We consider a "twisted" noncommutative join procedure for unital $C^*$-algebras which admit actions by a compact abelian group $G$ and its discrete abelian dual $\Gamma$, so that we may investigate an analogue of Baum-Dabrowski-Hajac…

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and…

Using an analogy between the Brauer groups in algebra and the Whitehead groups in topology, we first use methods of algebraic K-theory to give a natural definition of Brauer spectra for commutative rings, such that their homotopy groups are…

We construct multiplicative norms on equivariant nonconnective algebraic $K$-theory for finite groups $G$. We also construct a genuine equivariant version of THH equipped with a Dennis trace map from K-theory compatible with the…

Let $X$ be an irreducible smooth complex projective curve. Let ${\mathcal Q}(r,d)$ be the Quot scheme parametrizing all coherent subsheaves of ${\mathcal O}^{\oplus r}_X$ of rank $r$ and degree $-d$. There are natural morphisms ${\mathcal…

Given a smooth projective variety $M$ endowed with a faithful action of a finite group $G$, following Jarvis-Kaufmann-Kimura and Fantechi-G\"ottsche, we define the orbifold motive (or Chen-Ruan motive) of the quotient stack $[M/G]$ as an…

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M_C(r,L) be the coarse moduli space of semistable vector bundles…

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…