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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 4th 2013
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI 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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 4th 2013
   • (edited Feb 4th 2013)
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI have now edited [[local field]], mentioning alternative uses of this phrase, notably in Serre's _Corps Locaux_. More to come.

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

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 4th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexNice! I have now added some more hyperlinks and cross-links.

   Nice!

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