Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Number Theory

arXiv:2201.10136 (math)
[Submitted on 25 Jan 2022 (v1), last revised 14 Nov 2023 (this version, v3)]

Title:Hodge-Tate prismatic crystals and Sen theory

Authors:Hui Gao
View PDF
Abstract:Let $K$ be a mixed characteristic complete discrete valuation field with perfect residue field, and let $K_\infty/K$ be a Kummer tower extension by adjoining a compatible system of $p$-power roots of a chosen uniformizer. We use this Kummer tower to reconstruct Sen theory which classically is obtained using the cyclotomic tower. Using this Sen theory over the Kummer tower, we prove a conjecture of Min-Wang which predicts that Hodge-Tate prismatic crystals are determined by the Sen operator; this implies that the category of (rational) Hodge-Tate prismatic crystals is equivalent to the category of nearly Hodge-Tate representations.
Comments: All results in this preprint are now contained (as a subset) in the preprint 2311.07024 (which uses same title as this preprint). Please read that preprint instead. We apologize for confusions
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
Cite as: arXiv:2201.10136 [math.NT]
  (or arXiv:2201.10136v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.2201.10136

Submission history

From: Hui Gao [view email]
[v1] Tue, 25 Jan 2022 07:20:01 UTC (30 KB)
[v2] Tue, 21 Jun 2022 11:40:39 UTC (32 KB)
[v3] Tue, 14 Nov 2023 03:29:11 UTC (32 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.NT
< prev   |   next >
new | recent | 2022-01
Change to browse by:
math
math.AG

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)