Abstract Ulrich Derenthal

Ulrich Derenthal will speak on

Cox rings over nonclosed fields

Abstract: Universal torsors, introduced by Colliot-Thélène and Sansuc, can be used to study rational points on algebraic varieties. Cox constructed homogeneous coordinate rings for toric varieties, and generalizations of Cox's construction have been studied for varieties over algebraically closed fields. In this talk, we present a new definition of Cox rings and Cox sheaves for varieties over nonclosed fields. We discuss their existence and classification, and we make their relation to universal torsors precise.