A Serre-type spectral sequence for motivic cohomology

Abstract

In this paper, we construct and study a Serre-type spectral sequence for motivic cohomology associated to a map of bisimplicial schemes with motivically cellular fiber. Then, we show how to apply it in order to approach the computation of the motivic cohomology of the Nisnevich classifying space of projective general linear groups. This naturally yields an explicit description of the motive of a Severi-Brauer variety in terms of twisted motives of its Čech simplicial scheme.

Motivic cohomology of the Nisnevich classifying space of even Clifford groups

“…Following [8], we studied the motivic cohomology rings of the Nisnevich classifying spaces of unitary groups in [9], of spin groups in [11] and of projective general linear groups in [10]. This paper is a natural follow-up of [11].…”

Motivic cohomology of the Nisnevich classifying space of even Clifford groups

“…Following [7], we studied the motivic cohomology rings of the Nisnevich classifying spaces of unitary groups in [9], of spin groups in [10] and of projective general linear groups in [8]. This paper is a natural follow-up of [10].…”