Let A be a regular ring containing a field of characteristic zero and let \(R = A[X_1,\ldots , X_m]\). Consider R as standard graded with \(\deg A = 0\) and \(\deg X_i = 1\) for all i. In this paper we present a comprehensive study of graded components of local cohomology s \(H^i_I(R)\) where I is an arbitrary homogeneous ideal in R. Our study seems to be the first in this regard.

中文翻译：

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局部同调模块的分级组件

设A为包含特征为零的字段的正则环，设\（R = A [X_1，\ ldots，X_m] \）。考虑ř作为标准与分级\（\度A = 0 \）和\（\度X_I = 1 \）对于所有我。在本文中，我们对局部同构s （（H ^ i_I（R）\）的梯度分量进行了全面研究，其中I是R中的任意齐次理想。我们的研究似乎是这方面的第一篇论文。