The Picard Group of Brauer-Severi Varieties

Eslam Badr (1) , Francesc Bars (1) , Elisa Lorenzo García (2)

1 UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona
2 IRMAR - Institut de Recherche Mathématique de Rennes

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

Domaines: Théorie des nombres [math.NT]

Eslam Badr, Francesc Bars, Elisa Lorenzo García. The Picard Group of Brauer-Severi Varieties. Open Mathematics Journal, 2018, 16 (1), pp.1196-1203. ⟨10.1515/math-2018-0101⟩. ⟨hal-01618783⟩