Solid locally analytic representations

[2305.03162] Solid locally analytic representations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Representation Theory arXiv:2305.03162 (math) [Submitted on 4 May 2023 ( v1 ), last revised 3 Aug 2026 (this version, v5)] Title: Solid locally analytic representations Authors: Joaquín Rodrigues Jacinto , Juan Esteban Rodríguez Camargo View a PDF of the paper titled Solid locally analytic representations, by Joaqu\'in Rodrigues Jacinto and Juan Esteban Rodr\'iguez Camargo View PDF HTML (experimental) Abstract: We develop the $p$-adic representation theory of $p$-adic Lie groups on solid vector spaces over a complete non-archimedean extension of $\mathbb{Q}_p$. More precisely, we define and study categories of solid, solid locally analytic and solid smooth representations. We show that the category of solid locally analytic representations of a compact $p$-adic Lie group is equivalent to that of quasi-coherent modules over its algebra of locally analytic distributions, generalizing a classical result of Schneider and Teitelbaum. For arbitrary $G$, we prove an equivalence between solid locally analytic representations and quasi-coherent sheaves over certain locally analytic classifying stack over $G$. We also extend our previous cohomological comparison results from the case of a compact group defined over $\mathbb{Q}_p$ to the case of an arbitrary group, generalizing results of Lazard and Casselman-Wigner. Finally, we study an application to the locally analytic $p$-adic Langlands correspondence for $\mathrm{GL}_1$. Comments: 79 pages. Major revisions Subjects: Representation Theory (math.RT) ; Number Theory (math.NT) Report number: MPIM-Bonn-2023 Cite as: arXiv:2305.03162 [math.RT] (or arXiv:2305.03162v5 [math.RT] for this version) https://doi.org/10.48550/arXiv.2305.03162 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Joaquín Rodrigues Jacinto [ view email ] [v1] Thu, 4 May 2023 21:32:01 UTC (56 KB) [v2] Tue, 3 Oct 2023 17:39:46 UTC (74 KB) [v3] Thu, 13 Mar 2025 16:36:17 UTC (76 KB) [v4] Tue, 14 Apr 2026 09:23:53 UTC (80 KB) [v5] Mon, 3 Aug 2026 12:13:57 UTC (74 KB) Full-text links: Access Paper: View a PDF of the paper titled Solid locally analytic representations, by Joaqu\'in Rodrigues Jacinto and Juan Esteban Rodr\'iguez Camargo View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2023-05 Change to browse by: math math.NT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• An example of local analytic \(q\)-difference equation: analytic classification#301084
• Standard Representations of Crystallographic Coxeter Groups#927043
• Valeurs Dans la Representation Scientifique#97770
• Certified Topological Interaction in Neural Representations: Class Disentanglement Is Mostly Pairwise#985904
• The Unitarity of Arthur Packets for Real Reductive Groups#1117446