论文标题
Grothendieck-Serre的未受到的案例，用于完全各向同性的简单相互联系的组方案
Unramified case of Grothendieck-Serre for totally isotropic simply-connected group schemes
论文作者
论文摘要
我们证明了Grothendieck-serre的猜想：让$ r $成为Dedekind域上的Noetherian半固定式代数，使得所有$ r $的纤维都是几何定期的；让$ g $是具有严格适当的抛物线子组方案的简单连接的还原$ r $ $ group方案。然后，$ g $ torsor是微不足道的，前提是它比$ r $的总圆环是微不足道的。我们还简化了Quasisplit未受到的案例中的猜想的证明。该论点是基于我们介绍的一系列Torsors链的概念。我们还证明，如果$ r $是noetherian的普通域，而$ g $如上所述，那么，对于任何一般的tosor torsor而言，与spec $ r $ of Spec $ r $的开放子集$ u $相比，封闭的子集$ z $ spec $ r $的编辑至少两个，这样的torsor torsor对任何$ u-z $ abledials of $ u-z $ of $ z $。
We prove a case of the Grothendieck-Serre conjecture: let $R$ be a Noetherian semilocal flat algebra over a Dedekind domain such that all fibers of $R$ are geometrically regular; let $G$ be a simply-connected reductive $R$-group scheme having a strictly proper parabolic subgroup scheme. Then a $G$-torsor is trivial, provided that it is trivial over the total ring of fractions of $R$. We also simplify the proof of the conjecture in the quasisplit unramified case. The argument is based on the notion of a unipotent chain of torsors that we introduce. We also prove that if $R$ is a Noetherian normal domain and $G$ is as above, then for any generically trivial torsor over an open subset $U$ of Spec $R$, there is a closed subset $Z$ of Spec $R$ of codimension at least two such the torsor trivializes over any affine open of $U-Z$.
