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## Discussion Tag Cloud

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

• 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

• 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 $\mathbb{F}_p$ or “over $\mathbb{F}_1$”.

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?