The Picard group of Brauer-Severi varieties

Abstract

In this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi surfaces. To produce these generators we use the theory of twists of smooth plane curves.

Keywords

• brauer-severi varieties
• picard groups
• cyclic algebras
• theory of twists
• automorphisms
• 11g35
• 14j26
• 11d41
• 14j50
• 14j70
• 11r34