IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4614-5292-8_14.html
   My bibliography  Save this book chapter

F-Purity, Frobenius Splitting, and Tight Closure

In: Commutative Algebra

Author

Listed:
  • Melvin Hochster

    (University of Michigan, Department of Mathematics)

Abstract

Several applications of the technique of studying when the Frobenius endomorphism from a ring of positive prime characteristic to itself splits are discussed. These include some problems that, historically, motivated the development of the theory. One of these is the theorem that rings of invariants of linearly reductive groups acting on regular rings are Cohen-Macaulay, including normal rings generated by monomials. Another is the characterization of when Stanley-Reisner rings are Cohen-Macaulay. Another is the proof of the existence of finitely generated maximal Cohen-Macaulay modules for graded rings of positive prime characteristic when the normalization has an isolated singularity (or an isolated non-Cohen-Macaulay point), which includes all three-dimensional graded domains of positive characteristic. Applications of the closely related theory of tight closure are also discussed.

Suggested Citation

  • Melvin Hochster, 2013. "F-Purity, Frobenius Splitting, and Tight Closure," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, edition 127, pages 471-484, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5292-8_14
    DOI: 10.1007/978-1-4614-5292-8_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:sprchp:978-1-4614-5292-8_14. 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.