On the Grothendieck–Serre conjecture on principal bundles in mixed characteristic
| العنوان: | On the Grothendieck–Serre conjecture on principal bundles in mixed characteristic |
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| المؤلفون: | Roman Fedorov |
| المصدر: | Transactions of the American Mathematical Society |
| بيانات النشر: | American Mathematical Society (AMS), 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Large class, Pure mathematics, Conjecture, Applied Mathematics, General Mathematics, 010102 general mathematics, Principal (computer security), Local ring, Field (mathematics), Regular local ring, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 16. Peace & justice, 01 natural sciences, Mathematics - Algebraic Geometry, Scheme (mathematics), FOS: Mathematics, 0101 mathematics, Algebraic Geometry (math.AG), Quotient, Mathematics |
| الوصف: | Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. We prove the conjecture for a large class of regular local rings not containing fields in the case when G is split. Comment: The final version to be published in Transactions of the AMS. Results about quadratic forms are strengthened. In the section on Bertini type theorems a correction in the case of a non-perfect residue field is made. Other minor corrections and improvements |
| وصف الملف: | application/pdf |
| تدمد: | 1088-6850 0002-9947 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e3d697440240a9f5ad1a0d73df61928Test https://doi.org/10.1090/tran/8490Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....6e3d697440240a9f5ad1a0d73df61928 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10886850 00029947 |
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