论文标题
负面的同胞和琐碎模块的内态环
Negative cohomology and the endomorphism ring of the trivial module
论文作者
论文摘要
让$ k $成为特征$ 2 $的字段，让$ h $是有限的组或组计划。我们表明，负面泰特共同体$ \ wideHat {\ text {h}}^{\ leq 0}（\ leq 0}（h，k）$可以在$ kg $ -modules $ g $ h $ $ h $ $ h $ $ g $ h $ $ g $ h $ $ g $ h $ $ g $ h $ $ g $ g $ $ g $ g $ $ g $ h $的稳定类别中的琐事模块的内态戒指。这意味着在某些情况下，琐碎模块的内态性是一个局部环，无限生成的自由基为零。这与一些已知的计算形成了鲜明的对比，其中琐碎模块的内态环是该组共同体环的定位的零度。
Let $k$ be a field of characteristic $2$ and let $H$ be a finite group or group scheme. We show that the negative Tate cohomology ring $\widehat{\text{H}}^{\leq 0}(H,k)$ can be realized as the endomorphism ring of the trivial module in a Verdier localization of the stable category of $kG$-modules for $G$ an extension of $H$. This means in some cases that the endomorphism of the trivial module is a local ring with infinitely generated radical with square zero. This stands in stark contrast to some known calculations in which the endomorphism ring of the trivial module is the degree zero component of a localization of the cohomology ring of the group.
