IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v52y2021i4d10.1007_s13226-021-00042-7.html
   My bibliography  Save this article

Formal Schemes of Rational Degree

Author

Listed:
  • Harpreet Singh Bedi

    (Alfred University)

Abstract

Formal schemes in algebraic geometry consist of power series with integer degree, this idea can be naturally carried over to power series with rational degree. In this paper formal schemes with rational degree are constructed. These schemes are non noetherian and thus require slight modification of the standard approach. The first part of the paper constructs non noetherian continuous valuation rings from discrete valuation rings, and these rings are reffered to as ‘eka’ (one in Hindi) rings. These new rings are designed to carry the properties of discrete valuation to continuous valuation faithfully. The second part of the paper constructs non noetherian formal schemes with rational degree and shows their admissibility. The corresponding flatness and coherence is proved. Finally line bundles of rational degree are constructed and their Čech cohomology computed.

Suggested Citation

  • Harpreet Singh Bedi, 2021. "Formal Schemes of Rational Degree," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 1004-1020, December.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00042-7
    DOI: 10.1007/s13226-021-00042-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-021-00042-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-021-00042-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00042-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.