The dualizing module and top-dimensional cohomology group of $$\hbox {GL}_n(\mathcal {O})$$
The dualizing module and top-dimensional cohomology group of $$\hbox {GL}_n(\mathcal {O})$$
复制标题
$$hbox {GL}_n(mathcal {O})$$的对偶模块和顶维上同调群
DOI：
10.1007/s00209-021-02769-9
复制
发表时间：
2022
影响因子：
0.8
通讯作者：
Studenmund, Daniel
中科院分区：
文献类型：
--
作者：
Putman, Andrew;Studenmund, Daniel
For a number ring, Borel and Serre proved thatis a virtual duality group whose dualizing module is the Steinberg module. They also proved thatis a virtual duality group. In contrast to, we prove that the dualizing module ofis sometimes the Steinberg module, but sometimes instead is a variant that takes into account a sort of orientation. Using this, we obtain vanishing and nonvanishing theorems for the cohomology ofin its virtual cohomological dimension.
