Variations on a theme of groups splitting by a quadratic extension and Grothendieck-Serre conjecture for group schemes \(F_4\) with trivial \(g_3\) invariant (Q612976)
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scientific article; zbMATH DE number 5827440
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Variations on a theme of groups splitting by a quadratic extension and Grothendieck-Serre conjecture for group schemes \(F_4\) with trivial \(g_3\) invariant |
scientific article; zbMATH DE number 5827440 |
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Variations on a theme of groups splitting by a quadratic extension and Grothendieck-Serre conjecture for group schemes \(F_4\) with trivial \(g_3\) invariant (English)
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16 December 2010
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The author studies structure properties of reductive group schemes defined over a local ring and splitting over its étale quadratic extension. As an application he proves the Serre-Grothendieck conjecture on rationally trivial torsors over a local regular ring containing a field of characteristic 0 for group schemes of type \(F_4\) with trivial \(g_3\) invariant.
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linear algebraic groups
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exceptional groups
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torsors
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non-Abelian cohomology
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local regular rings
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Grothendieck-Serre conjecture
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