论文标题
本地化类别中琐碎模块的内态环
The endomorphism ring of the trivial module in a localized category
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Suppose that $G$ is a finite group and $k$ is a field of characteristic $p >0$. Let $\mathcal{M}$ be the thick tensor ideal of finitely generated modules whose support variety is in a fixed subvariety $V$ of the projectivized prime ideal spectrum $\operatorname{Proj} \operatorname{H}^*(G,k)$. Let $\mathcal{C}$ denote the Verdier localization of the stable module category $\operatorname{stmod}(kG)$ at $\mathcal{M}$. We show that if $V$ is a finite collection of closed points and if the $p$-rank every maximal elementary abelian $p$-subgroups of $G$ is at least 3, then the endomorphism ring of the trivial module in $\mathcal{C}$ is a local ring whose unique maximal ideal is infinitely generated and nilpotent. In addition, we show an example where the endomorphism ring in $\mathcal{C}$ of a compact object is not finitely presented as a module over the endomorphism ring of the trivial module.
