Chernousov, Vladimir An alternative proof of Scheiderer’s theorem on the Hasse principle for principal homogeneous spaces. (English) Zbl 0960.20024 Doc. Math. 3, 135-148 (1998). 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. Cited in 2 Documents 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 Keywords:fields of virtual cohomological dimension one; Hasse principle; principal homogeneous spaces; Chevalley groups Citations:Zbl 0846.20047; Zbl 0857.20024 PDFBibTeX XMLCite \textit{V. Chernousov}, Doc. Math. 3, 135--148 (1998; Zbl 0960.20024) Full Text: EuDML EMIS