Inventiones mathematicae

, Volume 197, Issue 1, pp 47–56 | Cite as

Unramified division algebras do not always contain Azumaya maximal orders

  • Benjamin Antieau
  • Ben Williams


We show that, in general, over a regular integral noetherian affine scheme X of dimension at least 6, there exist Brauer classes on X for which the associated division algebras over the generic point have no Azumaya maximal orders over X. Despite the algebraic nature of the result, our proof relies on the topology of classifying spaces of algebraic groups.


Division Algebra Central Simple Algebra Noetherian Scheme Azumaya Algebra Smooth Affine 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsThe University of Southern CaliforniaLos AngelesUSA

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