On the non-abelian 2-cohomology of regular models of Henselian local rings
Let \((A,m,k)\) be an excellent Henselian, local domain with \(k\) either finite, or separable closed. Let \(X\rightarrow \mathrm{Spec } A\) be a proper morphism with special fiber \(X_0\rightarrow \mathrm{Spec } k\) of dimension at most one. If \(X\) is regular and \(L\) is a \(X_{et}\)-lien that is locally representable by a simply connected semi-simple group then all classes of \(H^2(X_{et},L)\) are neutral. This completes the results of \textit{J.-L. Colliot-Thélène, M. Ojanguren, R. Parimala} [Proceedings of the international colloquium on algebra, arithmetic and geometry, Mumbai, India, January 4--12, 2000. Part I and II. New Delhi: Narosa Publishing House, published for the Tata Institute of Fundamental Research, Bombay. Stud. Math., Tata Inst. Fundam. Res. 16, 185--217 (2002; Zbl 1055.14019)]. If \(\dim \;A=2\), \(k\) is algebraically closed of equicharacteristic \(0\) and \(X\) is regular model of \(A\) then all classes of \(H^2(K,L)\), \(K=\mathrm{Frac }A\) are neutral.
scientific article; zbMATH DE number 5620672