Cox rings over nonclosed fields

Ulrich Derenthal, Hannover and IAS
Fine Hall 322

For varieties over algebraically closed fields, Cox rings were defined and studied by Cox, Hu, Keel, Hausen and others, generalizing the homogeneous coordinate ring of projective varieties. We discuss the definition, existence and classification of Cox rings over arbitrary fields and their arithmetic applications to parameterize rational and
integral points, for example on del Pezzo surfaces.