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arXiv · 2311.11989

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

Robin Bartlett
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Abstract

We show that loci of crystalline representations of $G_K$ for $K/\mathbb{Q}_p$ 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--M\'ezard on loci of potentially crystalline representations to irregular weights.

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Robin Bartlett. 2023-11-20. Irreducibility of some crystalline loci with irregular Hodge--Tate weights. https://arxiv.org/abs/2311.11989

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