标题： 分解不变场的对角线 显示英文标题

标题： Decomposing the Diagonals of Invariant Fields

摘要： 这项工作开始使用对角线分解作为一种工具，以研究有限群的不变域的有理性$G$。 我们的基域必须是特征 0，因为我们使用了Bertini定理。 我们采取的步骤是，首先定义并研究一个“开”的Chow零群版本。 其次，我们利用这一点将我们的研究转化为对$G$伽罗瓦扩张的Chow群的研究。 我们证明了一个“西洛”性质，从而在$G$的不变量与其西洛子群的不变量之间建立了联系。 特别是，我们证明如果$G$是一个有限群，其$p$西罗子群为$P$，$V$是一个忠实的$G$模块，并且$F(V)^P$有非平凡的不分裂上同调，则$F(V)^G$不是可收缩有理函数域。最后，我们证明了关于对角分解和通用除法代数中心的西罗型定理。 显示英文摘要

摘要： This work begins the process of using the decomposition of the diagonal as a tool for studying the rationality of invariant fields of finite groups $G$. Our ground field must be characteristic 0 because of the use we make of Bertini theorems. The steps we take are, first, defining and studying an "open" version of Chow zero. Second, we use this to translate our study to that of a Chow group of $G$ Galois extensions. We prove a "Sylow" property and thereby yield a connection between the invariants of $G$ and that of its Sylow subgroups. In particular, we show that if $G$ is a finite group with $p$ Sylow subgroup $P$, $V$ is a faithful $G$ module, and $F(V)^P$ has nontrivial unramified cohomology, then $F(V)^G$ is not retract rational. Finally, we prove Sylow type theorems for decomposition of the diagonal and the centers of generic division algebras.