Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
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半简单群的曲面和轴上有理单连接簇族
DOI：
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发表时间：
2008
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通讯作者：
J. Starr
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作者：
A. J. Jong;Xuhua He;J. Starr
在适当的假设下，我们证明了在代数闭域上的曲面函数域上定义的射影齐次簇 G/P 的形式具有有理点。该方法使用简单连通性的代数几何模拟来用投影线代替单位间隔。因此，我们完成了代数闭域上函数域的伽罗瓦上同调中塞尔猜想 II 的证明。
Under suitable hypotheses, we prove that a form of a projective homogeneous variety G/P defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an algebro-geometric analogue of simple connectedness replacing the unit interval by the projective line. As a consequence, we complete the proof of Serre’s Conjecture II in Galois cohomology for function fields over an algebraically closed field.