支持各种有理表示
Support varieties for rational representations
摘要：
我们引入了特征为$p > 0$的代数闭域$k$上指数型线性代数群$G$的有理表示的支撑簇.这些簇是$G$的所有1-参数子群的空间$V(G)$的闭子空间。函子$M \mapsto V(G)_M$满足有限群和其他有限群模式所满足的支撑簇的许多标准性质。此外，有一个密切的关系$V(G)_M$和家庭的支持品种$V_r(G)_M$通过限制$G$行动Frobenius内核$G_{(r)} \subset G$。这些支持品种似乎特别适合于调查的无限维理性$G$ -模块。
英文摘要：
We introduce support varieties for rational representations of a linear algebraic group $G$ of exponential type over an algebraically closed field $k$ of characteristic $p > 0$. These varieties are closed subspaces of the space $V(G)$ of all 1-parameter subgroups of $G$. The functor $M \mapsto V(G)_M$ satisfies many of the standard properties of support varieties satisfied by finite groups and other finite group schemes. Furthermore, there is a close relationship between $V(G)_M$ and the family of support varieties $V_r(G)_M$ obtained by restricting the $G$ action to Frobenius kernels $G_{(r)} \subset G$. These support varieties seem particularly appropriate for the investigation of infinite dimensional rational $G$-modules.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
