Connectedness of Kisin varieties associated to absolutely irreducible Galois representations.
- Resource Type
- Article
- Authors
- Chen, Miaofen; Nie, Sian
- Source
- Journal für die Reine und Angewandte Mathematik. Apr2022, Vol. 2022 Issue 785, p31-54. 24p.
- Subject
- *LOGICAL prediction
*MATHEMATICAL connectedness
- Language
- ISSN
- 0075-4102
We consider the Kisin variety associated to an n-dimensional absolutely irreducible mod p Galois representation ρ ¯ {\bar{\rho}} of a p-adic field K together with 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 ramified with n = 3 {n=3} or μ is of a very particular form. As an application, we get a connectedness result for the deformation ring associated to ρ ¯ {\bar{\rho}} of given Hodge–Tate weights. We also give counterexamples to show Kisin's conjecture does not hold in general. [ABSTRACT FROM AUTHOR]