Homogeneous spaces, algebraic K-theory and cohomological dimension of fields

Diego Izquierdo

In 1986, Kato and Kuzumaki stated a set of conjectures which aimed at giving a Diophantine characterization of the cohomological dimension of fields in terms of Milnor \(K\)-theory and points on projective hypersurfaces of small degree. Those conjectures are known to be wrong in general. In this talk, I will prove a variant of Kato and Kuzumaki's conjectures in which projective hypersurfaces of small degree are replaced by homogeneous spaces. This isjoint work with Giancarlo Lucchini Arteche.