论文标题
关于二次整数环的GL（3）的Farrell-Tate共同学
On Farrell-Tate cohomology of GL(3) over rings of quadratic integers
论文作者
论文摘要
本文的目的是推动算术组的Farrell-Tate共同体学计算前沿。循环亚组的共轭分类缩小为整数的合适环上的组环模块的分类，这些整数是主要理想域，从而概括了雷手的旧结果。作为Farrell-Tate共同学计算所需的数量理论输入的一个示例，我们详细讨论了PGL（3）中的同源扭转（3）对二次整数的主要理想环，并伴随着假想的二次情况下的机器计算。
The goal of the present paper is to push forward the frontiers of computations on Farrell-Tate cohomology for arithmetic groups. The conjugacy classification of cyclic subgroups is reduced to the classification of modules of group rings over suitable rings of integers which are principal ideal domains, generalizing an old result of Reiner. As an example of the number-theoretic input required for the Farrell-Tate cohomology computations, we discuss in detail the homological torsion in PGL(3) over principal ideal rings of quadratic integers, accompanied by machine computations in the imaginary quadratic case.
