IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v296y2023i3p1041-1055.html
   My bibliography  Save this article

Essential finite generation of extensions of valuation rings

Author

Listed:
  • Rankeya Datta

Abstract

Given a generically finite local extension of valuation rings V⊂W$V \subset W$, the question of whether W is the localization of a finitely generated V‐algebra is significant for approaches to the problem of local uniformization of valuations using ramification theory. Hagen Knaf proposed a characterization of when W is essentially of finite type over V in terms of classical invariants of the extension of associated valuations. Knaf's conjecture has been verified in important special cases by Cutkosky and Novacoski using local uniformization of Abhyankar valuations and resolution of singularities of excellent surfaces in arbitrary characteristic, and by Cutkosky for valuation rings of function fields of characteristic 0 using embedded resolution of singularities. In this paper, we prove Knaf's conjecture in full generality.

Suggested Citation

  • Rankeya Datta, 2023. "Essential finite generation of extensions of valuation rings," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1041-1055, March.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:3:p:1041-1055
    DOI: 10.1002/mana.202100190
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202100190
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202100190?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
    ---><---

    References listed on IDEAS

    as
    1. Steven Dale Cutkosky & Josnei Novacoski, 2021. "Essentially finite generation of valuation rings in terms of classical invariants," Mathematische Nachrichten, Wiley Blackwell, vol. 294(1), pages 15-37, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:bla:mathna:v:296:y:2023:i:3:p:1041-1055. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

      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.