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• CommentRowNumber1.
• CommentAuthorTodd_Trimble
• CommentTimeFeb 4th 2013

I added some material to Puiseux series, notable the proof that for $K$ algebraically closed of characteristic zero, they form the algebraic closure of the field of Laurent series $K((x))$. 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!