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

Heilbronn Number Theory Seminar

29th January 2020, 4:00 pm – 5:00 pm

Fry Building, 2.04

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 is joint work with Giancarlo Lucchini Arteche.

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