论文标题
模块的完整同胞中的尼尔肽和二元性
Nilpotence and Duality in the Complete Cohomology of a Module
论文作者
论文摘要
假设$ g $是一个有限的组，$ k $是特征$ p> 0 $的字段。我们考虑完整的同胞环$ \ mathcal {e} _m^* = \ sum_ {n \ in \ mathbb {z}}} \ wideHat {ext}^n_ {kg}（m，m，m）$。我们表明，戒指有两个杰出的理想$ i^*\ subseteq j^*\ subseteq \ mathcal {e} _m^*$，使得$ i^*$在上面以$ \ mathcal {e} _mm^*/j^*$为限制的$ i^*$ bunder和$ j^*$ diSIC bundies timper和$ j^*$。我们证明，如果$ m $既不是投影也不是周期性的，那么在$ \ Mathcal {e} _m^*$中以负一个负值为负的元素是一个nilpotent代数。
Suppose that $G$ is a finite group and $k$ is a field of characteristic $p>0$. We consider the complete cohomology ring $\mathcal{E}_M^* = \sum_{n \in \mathbb{Z}} \widehat{Ext}^n_{kG}(M,M)$. We show that the ring has two distinguished ideals $I^* \subseteq J^* \subseteq \mathcal{E}_M^*$ such that $I^*$ is bounded above in degrees, $\mathcal{E}_M^*/J^*$ is bounded below in degree and $J^*/I^*$ is eventually periodic with terms of bounded dimension. We prove that if $M$ is neither projective nor periodic, then the subring of all elements in negative degrees in $\mathcal{E}_M^*$ is a nilpotent algebra.
