Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 19th 2014

    created a minimum at global field

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeJul 20th 2014

    This seems unrelated to local field. That page already has a warning about terminology; should we add this?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 20th 2014

    Yes, should be added.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 20th 2014

    Rather than say “unrelated to”, I would say it’s “contrasted with” local field. Of course there are relations between the two; a global field is frequently analyzed in terms of its local field completions. What would the warning say?

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeJul 20th 2014

    The most basic warning is just to not think that the concepts are negations.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 20th 2014

    That’s what I figured; thanks.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 20th 2014
    • (edited Jul 20th 2014)

    I suppose the terminology originates in – or at least may be read in hindsight as – the fact that global fields are the fields which arise as global sections of the sheaf of rational functions on an arithmetic curve over 𝔽 p\mathbb{F}_p or “over 𝔽 1\mathbb{F}_1”.

    The Wikipedia entry kind of sort of gets in this direction in its historical paragraph, but is not too specific.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 21st 2014

    …as global sections…

    A term in some dependent product type then?

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)