On a motivic interpretation of primitive, variable and fixed cohomology

Caterads and Motivic Cohomology

We define “weighted multiplicative presheaves” and observe that there are several weighted multiplicative presheaves that give rise to motivic cohomology. By neglect of structure, weighted multiplicative presheaves give symmetric monoids of presheaves. We conjecture that a suitable stabilization of one of the symmetric monoids of motivic cochain presheaves has an action of a caterad of presheav...

An Overview of Motivic Cohomology

In this talk we give an overview of some of the motivations behind and applications of motivic cohomology.We first present aK-theoretic timeline converging onmotivic cohomology, then briefly discuss algebraic K-theory and its more concrete cousin Milnor K-theory. We then present a geometric definition of motivic cohomology via Bloch’s higher Chow groups and outline the main features of motivic ...

Equivariant Motivic Cohomology

The present paper will form part of the author’s PhD thesis, which will concern in part the practical computation of the motivic cohomology and the equivariant motivic cohomology of homogeneous varieties, such as Stiefel manifolds, Grassmanians, and spaces of matrices with prescribed rank conditions. Nothing proved here is particularly surprising, but it seems to the author that the spectral se...

On 2-torsion in motivic cohomology

On motivic cohomology with Z/l-coefficients