2002/06/15 by Daniel Krashen, Krashen, Daniel · 2 citations
Mathematics · #14m99 #15k20 #16s35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA #msc:14m99 #msc:15k20 #msc:16s35
paper · pdf · doi:10.48550/arxiv.math/0206154
22 pages
arxiv created 2002/06/15 · openalex publication_date 2002/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A conjecture of Amitsur states that two Severi-Brauer varieties are birationally isomorphic if and only if the underlying algebras are the same degree and generate the same cyclic subgroup of the Brauer group. It is known that generating the same cyclic subgroup is a necessary condition, however it has not yet been shown to be sufficient. In this paper we examine the case where the algebras have a maximal subfield K/F of degree n with Galois closure E/F whose Galois group is of the form Cn \rtimes H, where EH = K and |H| is prime to n. For such as we show that the conjecture is true for certain cases of n and H. In particular we prove the conjecture in the case that G is a dihedral group of order 2p, where p is prime