Unramified division algebras do not always contain azumaya maximal orders

Benjamin Antieau*, Ben Williams

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)47-56
Number of pages10
JournalInventiones Mathematicae
Issue number1
StatePublished - Jul 2014
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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