论文标题
同步和ext的排名在交叉特征中的一个有限的谎言类型
Cohomology and Ext for rank one finite groups of Lie type in cross characteristic
论文作者
论文摘要
我们计算$ \ operatoTorname {ext} _g^n（v，w）$的尺寸，用于所有不可约$ v $，$ w $，by $ r $ r $ -w $ blocks in $ r $ blocks of $ r $ blocks of Simple Groups $ \ properatoTorname {sz}（sz}（q）$，$ \ \ \ \ operatoRearnAme，$ \ \ operatoRearname {psu} $ $ \ operatatorName {{}^2G} _2（q）$ in Cross特征，特别是获得此类模块的所有共同体组的尺寸。在此过程中，我们还获得了任何$ r $ $ $ $ $ r $ block的循环缺陷的结果，其Brauer树是星形或线条（开放多边形）。
We compute the dimensions of $\operatorname{Ext}_G^n(V, W)$ for all irreducible $V$, $W$ lying in $r$-blocks of cyclic defect in the simple groups $\operatorname{Sz}(q)$, $\operatorname{PSU}_3(q)$ and $\operatorname{{}^2G}_2(q)$ in cross characteristic, obtaining in particular the dimensions of all cohomology groups for such modules. Along the way, we also obtain an analogous result for any $r$-block of cyclic defect whose Brauer tree is either a star or line (open polygon).
