Linkage of sets of cyclic algebras

Abstract

Let p be a prime integer and F the function field in two algebraically independent variables over a smaller field F 0 . We prove that if char ( F 0 ) = p ⩾ 3 then there exist p 2 − 1 cyclic algebras of degree p over F that have no maximal subfield in common, and if char ( F 0 ) = 0 then there exist p 2 cyclic algebras of degree p over F that have no maximal subfield in common.