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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Статьи
Orders that are étale-locally isomorphic
E. Bayer-Fluckigera, U. A. Firstb, M. Huruguena a Department of Mathematics, École Polytechnique Fédérale de Lausanne
b Department of Mathematics, University of Haifa
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 étale $R$-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 étale 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.
Ключевые слова:
hereditary order, maximal order, Dedekind domain, group scheme, reductive group, involution, central simple algebra.
Поступила в редакцию: 09.07.2018
Образец цитирования:
E. Bayer-Fluckiger, U. A. First, M. Huruguen, “Orders that are étale-locally isomorphic”, Алгебра и анализ, 31:4 (2019), 1–15; St. Petersburg Math. J., 31:4 (2020), 573–584
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1660 https://www.mathnet.ru/rus/aa/v31/i4/p1
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