A proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing infinite fields
A proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing infinite fields
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包含无限域的正则局部环上主丛的格洛腾迪克-塞尔猜想的证明
DOI：
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发表时间：
2012
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影响因子：
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通讯作者：
I. Panin
中科院分区：
文献类型：
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作者：
R. Fedorov;I. Panin
AbstractLet R$R$ be a regular local ring containing an infinite field. Let G$mathbf{G} $ be a reductive group scheme over R$R$. We prove that a principal G$mathbf{G} $-bundle over R$R$ is trivial if it is trivial over the fraction field of R$R$. In other words, if K$K$ is the fraction field of R$R$, then the map of non-abelian cohomology pointed sets
He´t1(R,G)→He´t1(K,G)$$H^{1}_{acute{mathrm{e}}mathrm{t}}(R,mathbf{G}) o H^{1}_{acute{mathrm{e}}mathrm{t}}(K, mathbf{G}) $$ induced by the inclusion of R$R$ into K$K$ has a trivial kernel.
AbstractLet R$R$ be a regular local ring containing an infinite field. Let G$mathbf{G} $ be a reductive group scheme over R$R$. We prove that a principal G$mathbf{G} $-bundle over R$R$ is trivial if it is trivial over the fraction field of R$R$. In other words, if K$K$ is the fraction field of R$R$, then the map of non-abelian cohomology pointed sets
He´t1(R,G)→He´t1(K,G)$$H^{1}_{acute{mathrm{e}}mathrm{t}}(R,mathbf{G}) o H^{1}_{acute{mathrm{e}}mathrm{t}}(K, mathbf{G}) $$ induced by the inclusion of R$R$ into K$K$ has a trivial kernel.