Quaternion Algebras with the Same Subfields

Part of the Developments in Mathematics book series (DEVM, volume 18)


Prasad and Rapinchuk asked if two quaternion divisionF-algebras that have the same subfields are necessarily isomorphic. The answer is known to be “no” for some very large fields. We prove that the answer is “yes” if F is an extension of a global field K so that FK is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields.


Division Algebra Quadratic Extension Quaternion Algebra Linear Algebraic Group Discrete Valuation Ring 


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© Springer New York 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Center for Communications Research-PrincetonPrincetonUSA

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