Products of Brauer Severi surfaces

2007/06/23 by Amit Hogadi, Hogadi, Amit · 1 citation
Engineering · Mathematics · #14E05 #14M99 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0706.3447

openalex publication_date 2007/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \P_i\_{1 ≤ i ≤ r} and \Q_i\_{1 ≤ i ≤ r} be two collections of Brauer Severi surfaces (resp. conics) over a field k. We show that the subgroup generated by the P_i's in Br(k) is the same as the subgroup generated by the Q_i's \iff ΠP_i is birational to ΠQ_i. Moreover in this case ΠP_i and ΠQ_i represent the same class in M(k), the Grothendieck ring of k-varieties. The converse holds if char(k)=0. Some of the above implications also hold over a general noetherian base scheme.

Cited by

• Birational equivalence of Severi-Brauer varieties

Related

• Severi-Brauer varieties of semidirect product algebras
• Quotients of Severi-Brauer surfaces
• Birational isomorphisms between generalized Severi-Brauer varieties
• A determinant on birational maps of Severi-Brauer surfaces
• Algebraic cycles on Severi-Brauer schemes of prime degree over a curve