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绝对不可约Galois表示的Kisin簇的连通性(聂思安)
2022-05-12 | 编辑:

  We consider the Kisin variety associated to a $n$-dimensional absolutely irreducible mod $p$ Galois representation $\bar\rho$ of a $p$-adic field $K$ and a cocharacter $\mu$. Kisin conjectured that the Kisin variety is connected in this case. We show that Kisin's conjecture holds if $K$ is totally ramfied with $n=3$ or $\mu$ is of a very particular form. As an application, we also get a connectedness result for the deformation ring associated to $\bar\rho$ of given Hodge-Tate weights. We also give counterexamples to show Kisin's conjecture does not hold in general. 

 

  Publication: 

  Journal für die reine und angewandte Mathematik (Crelles Journal) Volume 2022 Issue 785 

 

  Author: 

  Miaofen Chen 

  Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, No. 500, Dong Chuan Road, Shanghai 200241, China 

  E-mail: mfchen@math.ecnu.edu.cn 

    

  Sian Nie 

  Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, Zhongguancun East Road, Beijing 100190, China 

  E-mail: niesian@amss.ac.cn  

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