Unramified division algebras do not always contain Azumaya maximal orders

• 成果类型: Article
• 署名作者: Antieau, Benjamin; Williams, Ben
• 署名单位: University of California System; University of California Los Angeles; University of Southern California
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0479-7
• 发表日期: 2014
• 页码: 47-56
• 关键词: projective-modules

摘要

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.