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arXiv · 1509.02360

On the size of the genus of a division algebra

Vladimir I. Chernousov·Andrei S. Rapinchuk·Igor A. Rapinchuk
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Abstract

Let D be a central division algebra of degree n over a field K. One defines the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) of K represented by central division algebras D' of degree n over K having the same maximal subfields as D. We prove that if the field K is finitely generated and n is prime to its characteristic, then gen(D) is finite, and give explicit estimations of its size in certain situations.

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Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk. 2015-09-08. On the size of the genus of a division algebra. https://arxiv.org/abs/1509.02360

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