论文标题
Eisenstein扩展，连接性和第二个消失定理
Eisenstein extension, connectedness and the second vanishing theorem
论文作者
论文摘要
在本文中，首先，我们表明，对于不受影响的常规本地环$ r $的EISENSTEIN扩展，当理想的$ i $ $ s $扩展到理想的$ j $ j $ j $ j $ r $时，如果连接$ s/j $的$ r/j $连接到$ s/js $连接时，则是eisenstein的扩展。使用此功能，我们将SVT的结果扩展到仅针对扩展理想完成分支的常规局部环。如果$ s/js $的刺穿频谱被断开连接，则当每个最小的Primes $ \ p $ $ j $，$ r/\ p $都是正常的时，也会断开$ r/j $的连接。在这种情况下，我们证明他们两个都具有相同数量的连接组件。最后，我们表明，对于未受到的常规局部环（通过Eisenstein扩展为扩展的理想），两个最高的局部共同体学模块满足了\ cite {l-y}的猜想1，尽管猜想通常是错误的。
In this paper, at first, we show that for a ramified regular local ring $S$, which is an Eisenstein extension of an unramified regular local ring $R$, when an ideal $I$ of $S$ is extended from an ideal $J$ of $R$, the punctured spectrum of $R/J$ is connected if that of $S/JS$ is connected. Using this, we extend the result of SVT to complete ramified regular local ring only for the extended ideals. If the punctured spectrum of $S/JS$ is disconnected then that of $R/J$ is also disconnected when every minimal primes $\p$ of $J$, $R/\p$ is normal. Under this situation we prove that both of them have the same number of connected components. Finally, we show that for both unramified and ramified regular local rings (for extended ideal via Eisenstein extension), two top-most local cohomology modules satisfy the Conjecture 1 of \cite{L-Y}, although the conjecture is false in general.
