论文标题
$ \ ell $ - 模块化代表还原的$ thentime contrienta
The $\ell$-modular representation of reductive groups over finite local rings of length two
论文作者
论文摘要
令$ \ MATHCAL {O} _2 $和$ \ MATHCAL {O}'_ 2 $为两个不同的有限本地环，长度为二，残留的特征$ p $。令$ \ mathbb {g}（\ Mathcal {o} _2）$和$ \ Mathbb {g}（\ Mathcal {o}'_ 2）$，是任何还原组方案的点$ \ m athbb {g} $ bover $ \ nathbb { \ Mathbb {F} _Q $。我们证明，存在组的同构代数$ k [\ MATHBB {g}（\ Mathcal {o} _2）] \ cong k [\ Mathbb {g}（\ Mathcal {o}'_ 2）] $，其中$ K $与$ k $相同的大型字段与$ p $ p $ p $ p $。
Let $\mathcal{O}_2$ and $\mathcal{O}'_2$ be two distinct finite local rings of length two with residue field of characteristic $p$. Let $\mathbb{G}(\mathcal{O}_2)$ and $\mathbb{G}(\mathcal{O}'_2)$, be the group of points of any reductive group scheme $\mathbb{G}$ over $\mathbb{Z}$ such that $p$ is very good for $\mathbb{G} \times \mathbb{F}_q$. We prove that there exists an isomorphism of group algebra $K[\mathbb{G}(\mathcal{O}_2)] \cong K[\mathbb{G}(\mathcal{O}'_2)]$, where $K$ is a sufficiently large field of characteristic different from $p$.
