Irreducibility of some crystalline loci with irregular Hodge--Tate weights

2023/11/20 by Bartlett, Robin
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.11989

Abstract

We show that loci of crystalline representations of G_K for K/ℚ_p an unramified extension are irreducible when the Hodge--Tate weights are fixed and sufficiently small. This was previously known for weights in the interval [-p,0] and in this paper we show how that this bound can be relaxed provided the Hodge--Tate weights are sufficiently irregular at certain embeddings. This is motivated by the desire to extend the conjectures of Breuil--Mézard on loci of potentially crystalline representations to irregular weights.

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