Linkage of Sets of Cyclic Algebras

2021/04/16 by Chapman, Adam
#16K20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2104.08349

Abstract

Let p be a prime integer and F the function field in two algebraically independent variables over a smaller field F₀. We prove that if char(F₀)=p≥ 3 then there exist p²-1 cyclic algebras of degree p over F that have no maximal subfield in common, and if char(F₀)=0 then there exist p² cyclic algebras of degree p over F that have no maximal subfield in common.

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