Coniveau filtration and mixed motives

TL;DR

This paper introduces a new coniveau filtration framework within mixed motives, providing a universal spectral sequence construction and explicit differential computations, extending classical results in motivic cohomology.

Contribution

It develops the motivic coniveau exact couple in mixed motives and computes its differentials explicitly, extending classical Bloch-Ogus results.

Findings

Computed differentials in the coniveau spectral sequence using residues and transfers.

Unified the construction of coniveau spectral sequences across realizations.

Extended classical results of Bloch and Ogus to the motivic setting.

Abstract

We introduce the motivic coniveau exact couple of a smooth scheme, in the framework of mixed motives, whose property is to universally give rise to coniveau spectral sequences through realizations. The main result is a computation of its differentials in terms of residues and transfers of mixed motives, with a formula analog to the one defining the Weil divisor of a rational function. We then show how to recover and extend classical results of Bloch and Ogus for motivic realizations.