论文标题
与绝对不可还原的Galois表示相关的Kisin品种的连接性
Connectedness of Kisin varieties associated to absolutely irreducible Galois representations
论文作者
论文摘要
我们认为Kisin品种与$ n $ dimensional的绝对不可减至的mod $ p $ galois代表$ \barρ$ a $ p $ - adic field $ k $和cocharacter $ $ $ $。 Kisin猜想在这种情况下，Kisin品种已连接。我们表明，如果$ k $完全被$ n = 3 $或$μ$完全冲突，那么基斯的猜想就会存在。作为一个应用程序，我们还获得了与给定的hodge-tate权重的$ \barρ$相关的变形环的连接结果。我们还提供反例，以表明Kisin的猜想一般不存在。
We consider the Kisin variety associated to a $n$-dimensional absolutely irreducible mod $p$ Galois representation $\barρ$ of a $p$-adic field $K$ and a cocharacter $μ$. 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 $μ$ is of a very particular form. As an application, we also get a connectedness result for the deformation ring associated to $\barρ$ of given Hodge-Tate weights. We also give counterexamples to show Kisin's conjecture does not hold in general.
