?-cohomologically rigid local systems are integral
?-cohomologically rigid local systems are integral
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?-上同调刚性局部系统是积分的
DOI：
10.1090/tran/8610
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发表时间：
2022
影响因子：
1.3
通讯作者：
Patrikis, Stefan
中科院分区：
文献类型：
--
作者：
Klevdal, Christian;Patrikis, Stefan
设一个约化群，设一个光滑拟射影复簇。证明了具有有限阶阿贝尔化和拟单幂局部单点的任意不可约、上同刚性局部系统是积分的。这概括了Esnault和Groechenig[精选数学]的工作。（NS） 24 (2018), pp. 4279-4292；数学学报，225 (2020),pp. 103-158]，它肯定地回答了Simpson的一个猜想[Inst. Hautes Études Sci。出版。数学。75(1992)，第5-95页；高等学院Études科学出版。数学，80 (1994),pp. 5-79]。在此过程中，我们证明了任何这样的局部系统的单群的zariski闭包的连通分量是半简单的；当我们将上同刚性放宽为刚性时，这一点也成立。参考文献
Letbe a reductive group, and letbe a smooth quasi-projective complex variety. We prove that any-irreducible,-cohomologically rigid local system onwith finite order abelianization and quasi-unipotent local monodromies is integral. This generalizes work of Esnault and Groechenig [Selecta Math.(NS) 24 (2018), pp. 4279–4292; Acta Math. 225 (2020), pp. 103–158] when, and it answers positively a conjecture of Simpson [Inst. Hautes Études Sci. Publ. Math. 75 (1992), pp. 5–95; Inst. Hautes Études Sci. Publ. Math. 80 (1994), pp. 5–79] for-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; this moreover holds when we relax cohomological rigidity to rigidity. References