On quaternion algebras over some extensions of quadratic number fields

2020/04/01 by Acciaro, Vincenzo, Savin, Diana, Taous, Mohammed +1
#11R11 #11R21 #11R32 #11R52 #11S15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.01040

Abstract

Let p and q be two positive primes. Let ℓ be an odd positive prime integer and F a quadratic number field. Let K be an extension of F such that K is a dihedral extension of \Q of degree ℓ over F or K is an abelian ℓ-extension unramified over F assuming ℓ divides the class number of F. In this paper, we obtain a complete characterization of division quaternion algebras H_K(p, q) over K.

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