Coniveau filtration and mixed motives

Source abstract

We introduce the motivic coniveau exact couple associated with a smooth scheme, in the framework of mixed motives, whose property is to universally give rise to coniveau spectral sequences through realizations. Our main result is a computation of its differentials in terms of residues and transfers of mixed motives, by 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.