English

Breuil-Kisin modules and integral $p$-adic Hodge theory

Number Theory 2025-04-09 v6

Abstract

We construct a category of Breuil-Kisin GKG_K-modules to classify integral semi-stable Galois representations. Our theory uses Breuil-Kisin modules and Breuil-Kisin-Fargues modules with Galois actions, and can be regarded as the algebraic avatar of the integral pp-adic cohomology theories of Bhatt-Morrow-Scholze and Bhatt-Scholze. As a key ingredient, we classify Galois representations that are of finite E(u)E(u)-height.

Keywords

Cite

@article{arxiv.1905.08555,
  title  = {Breuil-Kisin modules and integral $p$-adic Hodge theory},
  author = {Hui Gao},
  journal= {arXiv preprint arXiv:1905.08555},
  year   = {2025}
}

Comments

final version. (slight typographical difference with journal version)

R2 v1 2026-06-23T09:15:04.193Z