On a generalization of the Picard-Brauer exact sequence, by Cristian D. Gonzalez-Aviles

We extend an argument of S.Lichtenbaum and obtain a generalization of the well-known Picard-Brauer exact sequence for a smooth variety X. The resulting exact sequence connects the codimension n Chow group of X with a certain "Brauer-like" group. As applications, we obtain a number of results on codimension 2 and codimension 3 cycles on various types of varieties (e.g., rational ones). We also give applications to projective homogeneous varieties.

Cristian D. Gonzalez-Aviles <gonzomat2002@yahoo.es>