Connectedness of Kisin varieties associated to absolutely irreducible Galois representations
- Resource Type
- Working Paper
- Authors
- Chen, Miaofen; Nie, Sian
- Source
- Subject
- Mathematics - Algebraic Geometry
Mathematics - Number Theory
- Language
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.
Comment: 19 pages