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An alternative proof of Scheiderer’s theorem on the Hasse principle for principal homogeneous spaces. (English) Zbl 0960.20024

Summary: We give an alternative proof of the Hasse principle for principal homogeneous spaces defined over fields of virtual cohomological dimension at most one which is based on a special decomposition of elements in Chevalley groups.

MSC:

20G15 Linear algebraic groups over arbitrary fields
20G10 Cohomology theory for linear algebraic groups
11E72 Galois cohomology of linear algebraic groups
11E04 Quadratic forms over general fields
14M17 Homogeneous spaces and generalizations
11E57 Classical groups
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