On cohomology groups $ H^{1} $ of $ G-$modules of finite type over cyclic groups

[1507.02370] On cohomology groups $ H^{1} $ of $ G-$modules of finite type over cyclic groups Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:1507.02370 (math) [Submitted on 9 Jul 2015 ( v1 ), last revised 18 May 2016 (this version, v2)] Title: On cohomology groups $ H^{1} $ of $ G-$modules of finite type over cyclic groups Authors: Derong Qiu View a PDF of the paper titled On cohomology groups $ H^{1} $ of $ G-$modules of finite type over cyclic groups, by Derong Qiu View PDF HTML (experimental) Abstract: Let $ G $ be a cyclic group, in this paper, we study the Herbrand quotient and $ 1-$th cohomology group on finitely generated $ G-$modules in some cases. When $ G $ is of order $ 2, $ the order of the cohomology group is explicitly related to some invariants, and this relation is used to study unit groups over quadratic extensions of number fields. We also give some applications on Pell equations and class number of number fields. Comments: 14 pages Subjects: Number Theory (math.NT) MSC classes: 11R11, 11R27, 11R29 11R11, 11R27, 11R29 Cite as: arXiv:1507.02370 [math.NT] (or arXiv:1507.02370v2 [math.NT] for this version) https://doi.org/10.48550/arXiv.1507.02370 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Advances and Applications in Mathematical Sciences, Vol.24, Issue9-10, (2025), 69-81 Submission history From: Derong Qiu [ view email ] [v1] Thu, 9 Jul 2015 04:40:35 UTC (7 KB) [v2] Wed, 18 May 2016 04:51:22 UTC (9 KB) Full-text links: Access Paper: View a PDF of the paper titled On cohomology groups $ H^{1} $ of $ G-$modules of finite type over cyclic groups, by Derong Qiu View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2015-07 Change to browse by: math 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

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