An Alternative Proof of Scheiderer's Theorem on the Hasse Principle for Principal Homogeneous Spaces

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.

1991 Mathematics Subject Classification: Primary 20G10; Secondary 11E72, 12D15.

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