Rigid connections on P1 via the Bruhat–Tits building
Rigid connections on P1 via the Bruhat–Tits building
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通过 Bruhat-Tits 大楼在 P1 上进行刚性连接
DOI：
10.1112/plms.12346
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发表时间：
2019
影响因子：
1.8
通讯作者：
Daniel S. Sage
中科院分区：
文献类型：
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作者：
Masoud Kamgarpour;Daniel S. Sage
我们应用Bremer和Sage的基本层理论，找到了射影直线上的上同调刚性G-联络，推广了Frenkel和Gross的工作。在这一理论中，我们研究了与Bruhat-Tits建筑中的一点有关的Moy-Prasad过滤的形式联系的先导项。如果引导项是正则半单的，且中心子是一个(不一定是分裂的)极大环面S，则我们有一个S环路。在这种语言中，Frenkel-Gross连接的不规则奇异性导致了与Coxeter环面C相关的最小斜率的齐次横向连接。本文考虑GM上的联络，这里h是Coxeter数，i是h的正整数互素，且在无穷远处具有单幂等正则奇点，在斜率i/h的零点处具有不规则齐次C轴奇点。我们的主要结果是描述了所有这种刚性联系的特征。
We apply the theory of fundamental strata of Bremer and Sage to find cohomologically rigid G ‐connections on the projective line, generalising the work of Frenkel and Gross. In this theory, one studies the leading term of a formal connection with respect to the Moy–Prasad filtration associated to a point in the Bruhat–Tits building. If the leading term is regular semisimple with centraliser a (not necessarily split) maximal torus S , then we have an S ‐toral connection. In this language, the irregular singularity of the Frenkel–Gross connection gives rise to the homogeneous toral connection of minimal slope associated to the Coxeter torus C . In the present paper, we consider connections on Gm which have an irregular homogeneous C ‐toral singularity at zero of slope i/h , where h is the Coxeter number and i is a positive integer coprime to h , and a regular singularity at infinity with unipotent monodromy. Our main result is the characterisation of all such connections which are rigid.