Connectedness of Kisin varieties associated to absolutely irreducible Galois representations

2020/07/14 by Miaofen Chen, Chen, Miaofen, Sian Nie +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2007.06861

19 pages

arxiv created 2020/07/14 · arxiv updated 2020/07/15

Abstract

We consider the Kisin variety associated to a n-dimensional absolutely irreducible mod p Galois representation ρ 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 ρ of given Hodge-Tate weights. We also give counterexamples to show Kisin's conjecture does not hold in general.

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