Connectedness of Kisin varieties associated to absolutely irreducible Galois representations

Abstract: Abstract: Let $K$ be a $p$-adic field. Let $\rho$ be an $n$-dimensional continuous absolutely irreducible mod $p$ representation of the absolute Galois group of $K$. The Kisin variety is a projective scheme which parametrizes the finite flat group schemes over the ring of integers of $K$ with generic fiber $\rho$ satisfying some determinant condition. The connected components of the Kisin variety is in bijection with the connected components of the generic fiber of the flat deformation ring of $\rho$ with given Hodge-Tate weights. Kisin conjectured that the Kisin variety is connected in this case. We show that Kisin's conjecture holds if $K$ is totally ramified with $n=3$ or the determinant condition is of a very particular form. We also give counterexamples to show Kisin's conjecture does not hold in general. This is a joint work with Sian Nie.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Comments: Please note that this talk is one hour earlier than usual.

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.