$\mathbb{Z}_p$-lattices in semistable Galois representations

Zijian Yao

$\mathbb{Z}_p$-lattices in semistable Galois representations

Number Theory 2023-08-30 v1 Algebraic Geometry

Authors: Zijian Yao

Abstract

We show that the category of logarithmic prismatic F-crystals on $(\mathcal{O}_K, \varpi^{\mathbb{N}})$ is equivalent to the category of $\mathbb{Z}_p$ -lattices in semistable $\text{Gal}_K$ -representations. We then apply our method to describe such Galois representations using linear algebraic data via various "logarithmic" versions of Breuil--Kisin modules.

Keywords

zp-lattices semistable galois representations logarithmic prismatic f-crystals breuil-kisin modules gal_k-representations

Cite

@article{arxiv.2308.15468,
  title  = {$\mathbb{Z}_p$-lattices in semistable Galois representations},
  author = {Zijian Yao},
  journal= {arXiv preprint arXiv:2308.15468},
  year   = {2023}
}

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