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    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 4th 2013

    I added some material to Puiseux series, notable the proof that for KK algebraically closed of characteristic zero, they form the algebraic closure of the field of Laurent series K((x))K((x)). This is to be connected with a number of unwritten topics like Hensel’s lemma, Newton polygon, complete local ring, and others.

    Meanwhile, I noticed that the term “local field” has, besides physics meanings, two closely related distinct mathematical meanings. One for which we have a page local field is (non-discrete) “locally compact Hausdorff topological field”, but another is “field of fractions of a complete DVR”. It’s somewhat strange that two such closely related but distinct concepts have the same name – a terrible source of confusion.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 4th 2013
    • (edited Feb 4th 2013)

    I have now edited local field, mentioning alternative uses of this phrase, notably in Serre’s Corps Locaux. More to come.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2013

    Nice!

    I have now added some more hyperlinks and cross-links.