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Splitting fields for \(E_8\)-torsors. (English) Zbl 1048.11031
The author shows that every torsor for the split algebraic group \(E_8\) over a field becomes trivial over some separable extension of degree dividing \(2^6\cdot 3^2\cdot 5= 2880\). This improves a bound \((2^9\cdot 3^3\cdot 5= 69120)\) by J. Tits [C. R. Acad. Sci., Paris, Sér. I 315, No. 11, 1131–1138 (1992; Zbl 0823.20042)] and, by the author’s computation of Grothendieck’s torsion index of \(E_8\), it turns out that the author’s bound is optimal.

MSC:
11E72 Galois cohomology of linear algebraic groups
14M17 Homogeneous spaces and generalizations
20G15 Linear algebraic groups over arbitrary fields
Software:
GAP
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References:
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