2002/03/13 by Daniel Krashen, Krashen, Daniel
Mathematics · #14E05 #16K20 #16K50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.AG #math.RA #msc:14E05 #msc:16K20 #msc:16K50
paper · pdf · doi:10.48550/arxiv.math/0203117
25 pages
arxiv created 2002/03/13 · openalex publication_date 2002/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to investigate the birational geometry of Generalized Severi-Brauer varieties. A conjecture of Amitsur states that two Severi-Brauer varieties V(A) and V(B) are birational if the underlying central simple algebras A and B are the same degree and generate the same cyclic subgroup of the Brauer group. We present a generalization of this conjecture to Generalized Severi-Brauer varieties, and show that in most cases we may reduce the new conjecture to the case where every subfield of the algebras is maximal, and in particular to the case where the algebras have prime power degree. This allows us to prove infinitely many new cases for Amitsur's original conjecture. We also give a proof of the generalized conjecture for the case B ≅ Aop.