The Emerton--Gee stack of rank one $(\varphi,\Gamma)$-modules
Dat Pham

TL;DR
This paper classifies rank one $(,g)$-modules over $p$-adic rings, providing a new proof and explicit description of the Emerton--Gee stack in this case, and extends results to étale $$-modules.
Contribution
It offers a new classification method for rank one $(,g)$-modules and generalizes existing results to étale $$-modules without $g$-action.
Findings
Explicit description of the Emerton--Gee stack for rank one modules
New proof of a key proposition in Emerton--Gee's work
Extension of results to étale $$-modules without $g$-action
Abstract
We give a classification of rank one -modules with coefficients in a -adically complete -algebra. As a consequence, we obtain a new proof of Proposition 7.2.17 in {arXiv:1908.07185}, which gives an explicit description of the Emerton--Gee stack of -modules in the rank one case. In fact, our method also applies in the context of rank one \' etale -modules (i.e. in the absence of a -action), generalizing another result of Emerton--Gee.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research
