TY - JOUR
T1 - Unramified division algebras do not always contain azumaya maximal orders
AU - Antieau, Benjamin
AU - Williams, Ben
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2013
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2014/7
Y1 - 2014/7
N2 - 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.
AB - 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.
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U2 - 10.1007/s00222-013-0479-7
DO - 10.1007/s00222-013-0479-7
M3 - Article
AN - SCOPUS:85027917610
VL - 197
SP - 47
EP - 56
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 1
ER -