论文标题
在算术雪佛兰群体的顶级共同体学上
On the top-dimensional cohomology of arithmetic Chevalley groups
论文作者
论文摘要
令$ \ mathbb {k} $为一个数字字段，带有整数$ \ mathfrak {o} $，让$ \ mathcal {g} $是chevalley组方案，而不是类型$ \ mathtt {e} {e} _8 _8 $，$ \ mathtt {f} _4 $ $或$ \ mathtt $} $ {g}。我们使用山雀建筑物的理论和Steinberg模块上的Tóth的结果来证明$ h^{\ propatotorname {vcd}}}}（\ Mathcal {g}（\ Mathfrak {o} {O}）
Let $\mathbb{K}$ be a number field with ring of integers $\mathfrak{O}$ and let $\mathcal{G}$ be a Chevalley group scheme not of type $\mathtt{E}_8$, $\mathtt{F}_4$ or $\mathtt{G}_2$. We use the theory of Tits buildings and a result of Tóth on Steinberg modules to prove that $H^{\operatorname{vcd}}(\mathcal{G}(\mathfrak{O}); \mathbb{Q}) = 0$ if $\mathfrak{O}$ is Euclidean.
