Abstract
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 language | English |
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Pages (from-to) | 573-584 |
Number of pages | 12 |
Journal | St. Petersburg Mathematical Journal |
Volume | 31 |
Issue number | 4 |
DOIs | |
State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Mathematical Society.
Keywords
- 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