论文标题
G-Rigid本地系统是不可或缺的
G-rigid local systems are integral
论文作者
论文摘要
令$ g $为一个还原的组，让$ x $成为一种流畅的准标记复合物。我们证明，任何$ g $ irreducible，$ g $ - 在$ x $上具有有限订单的abelianization和Quasi Unipotent的本地单体粒子的$ g $ - 生物学上的刚性本地系统都是不可或缺的。当$ g = \ mathrm {gl} _n $时，这概括了esnault和groechenig的工作，并且它以$ g $ - g $ - 物种学上僵化的本地系统的猜想，对辛普森的猜想积极回答。在此过程中，我们表明，任何此类局部系统的单型群的Zariski闭合组件的连接成分都是半神经。
Let $G$ be a reductive group, and let $X$ be a smooth quasi-projective complex variety. We prove that any $G$-irreducible, $G$-cohomologically rigid local system on $X$ with finite order abelianization and quasi-unipotent local monodromies is integral. This generalizes work of Esnault and Groechenig when $G= \mathrm{GL}_n$, and it answers positively a conjecture of Simpson for $G$-cohomologically rigid local systems. Along the way we show that the connected component of the Zariski-closure of the monodromy group of any such local system is semisimple.
