Cohomology over Fiber products of local rings
Cohomology over Fiber products of local rings
复制标题
局部环光纤积的上同调
DOI：
10.1016/j.jalgebra.2008.10.015
复制
发表时间：
2009
影响因子：
0.9
通讯作者：
W. Moore
中科院分区：
文献类型：
--
作者：
W. Moore
设S和T是具有公共剩余域k的局部环，R是纤维积S×kT，M是S-模. M的庞加莱级数PMR由Kostrikin和Shafarevich以及Dress和Krämer用PMS、PkSand PkT表示。在这里，一个显式的最小分辨率，以及定理的结构ExtR（k，k）和ExtR（M，k）的照明这些等式。给出了模的纤维积的上同调模的结构定理。作为这些结果的应用，我们计算了纤维积上的上同调模的深度。
Let S and T be local rings with common residue field k, let R be the fiber product S×kT, and let M be an S-module. The Poincaré series PMRof M has been expressed in terms of PMS, PkSand PkTby Kostrikin and Shafarevich, and by Dress and Krämer. Here, an explicit minimal resolution, as well as theorems on the structure of ExtR(k,k) and ExtR(M,k) are given that illuminate these equalities. Structure theorems for the cohomology modules of fiber products of modules are also given. As an application of these results, we compute the depth of cohomology modules over a fiber product.