2007/04/25 by Daniel Krashen, Krashen, Daniel
Computer Science · Mathematics · #16K20 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.RA #msc:16K20
paper · pdf · doi:10.48550/arxiv.0704.3443
13 pages
arxiv created 2007/04/25 · openalex publication_date 2007/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a field F, an étale extension L/F and an Azumaya algebra A/L, one knows that there are extensions E/F such that A ⊗F E is a split algebra over L ⊗F E. In this paper we bound the degree of a minimal splitting field of this type from above and show that our bound is sharp in certain situations, even in the case where L/F is a split extension. This gives in particular a number of generalizations of the classical fact that when the tensor product of two quaternion algebras is not a division algebra, the two quaternion algebras must share a common quadratic splitting field. In another direction, our constructions combined with results of Karpenko also show that for any odd prime number p, the generic algebra of index pn, and exponent p cannot be expressed nontrivially as the corestriction of an algebra over any extension field if n < p2.