论文标题
在环上进行组动作的模块结构
The Module Structure of a Group Action on a Ring
论文作者
论文摘要
考虑一个有限的组$ g $在分级的noetherian $ k $ -algebra $ s $上作用，对于某些特征性$ p $的字段$ k $；例如，$ s $可能是多项式环。将$ s $视为$ kg $ - 模块，并将特定不可兼容的模块的多样化视为每个度的汇总。我们展示了如何用同源代数以及如何将其与$ S $频谱的小组动作的几何形状相关联。
Consider a finite group $G$ acting on a graded Noetherian $k$-algebra $S$, for some field $k$ of characteristic $p$; for example $S$ might be a polynomial ring. Regard $S$ as a $kG$-module and consider the multiplicity of a particular indecomposable module as a summand in each degree. We show how this can be described in terms of homological algebra and how it is linked to the geometry of the group action on the spectrum of $S$.
