Breuil–Kisin modules and integral -adic Hodge theory (with Appendix A by Yoshiyasu Ozeki, and Appendix B by Hui Gao and Tong Liu)
Hui Gao
Southern University of Science and Technology, Shenzhen, China
![Breuil–Kisin modules and integral $p$-adic Hodge theory (with Appendix A by Yoshiyasu Ozeki, and Appendix B by Hui Gao and Tong Liu) cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-25-issue-10.png&w=3840&q=90)
Abstract
We construct a category of Breuil–Kisin -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 -adic cohomology theories of Bhatt–Morrow–Scholze and Bhatt–Scholze. As a key ingredient, we classify Galois representations that are of finite -height.
Cite this article
Hui Gao, Breuil–Kisin modules and integral -adic Hodge theory (with Appendix A by Yoshiyasu Ozeki, and Appendix B by Hui Gao and Tong Liu). J. Eur. Math. Soc. 25 (2023), no. 10, pp. 3979–4032
DOI 10.4171/JEMS/1278