Some split symbol algebras of prime degree

2020/03/06 by Diana Savin, Savin, Diana, Vincenzo Acciaro +1
Mathematics · #11A51 #11F85 #11R04 #11R18 #11R29 #11R37 #11R52 #11R54 #11S15 #11S20 #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11A51 #msc:11F85 #msc:11R04 #msc:11R18 #msc:11R29 #msc:11R37 #msc:11R52 #msc:11R54 #msc:11S15 #msc:11S20

paper · pdf · doi:10.48550/arxiv.2003.03082

arxiv created 2020/12/27 · arxiv updated 2020/12/29

Abstract

Let p be an odd prime, let K=ℚ(ε) where ε is a primitive cubic root of unity, and let L be the Kummer field ℚ(ε, √[3]α). In this paper we obtain a characterization of the splitting behavior of the symbol algebras ( (α,p)/(K,ε)) and ( \fracα,p^h_pK,ε), where h_p is the order in the class group Cl(L) of a prime ideal of O_L which divides pO_L.

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