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Статья «ORDERS THAT ARE ETALE-LOCALLY ISOMORPHIC, "Алгебра и анализ"»

Авторы:
  • BAYER-FLUCKIGER E.1
  • FIRST U. A.2
  • HURUGUEN M.3
стр. 1-15
Платно
1 Ecole Polvtechnique Federate de Lausanne, 2 University of Haifa, 3 Ecole Polvtechnique Federate de Lausanne
  • SDI: 007.001.0234-0852.2019.031.004.1
Ключевые слова:
  • hereditary order
  • maximal order
  • Dedekind domain
  • group scheme
  • reductive group
  • involution
  • central simple algebra
Аннотация:
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.

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