Orders that are etale-locally isomorphic

E. Bayer-Fluckiger, U. A. First, M. Huruguen

Research output: Contribution to journalArticlepeer-review


Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat etale R-algebra are isomorphic. On the other hand, this fails for hereditary orders with involution. The latter stands in contrast to a result of the first two authors, who proved this statement for Hermitian forms over hereditary R-orders with involution. The results can be restated by means of etale cohomology and can be viewed as variations of the Grothendieck-Serre conjecture on principal homogeneous spaces of reductive group schemes. The relationship with Bruhat-Tits theory is also discussed.

Original languageEnglish
Pages (from-to)573-584
Number of pages12
JournalSt. Petersburg Mathematical Journal
Issue number4
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society.


  • Central simple algebra
  • Dedekind domain
  • Group scheme
  • Hereditary order
  • Involution
  • Maximal order
  • Reductive group

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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