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First talk

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Errata

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WP is not a web host, nor a place to publish erratas, so I have removed it. Just in case it is of any use elsewhere - maybe WikiBooks?... - and as it looks like a good job, I'll preserve it here - Nabla (talk) 14:30, 6 April 2009 (UTC)[reply]

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Errata

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Chapter 1

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  • section 4, pg. 14, 2nd centered display: the ramification indices should be not in the product.
  • section 5, pg. 15, first formula needs to be , Not the other way around.
  • section 6, pg. 17, last sentence of first paragraph, replace the inclusion symbol with the word "in". Clearly, f is an element of A[X] and not an element of k[X]. In the French ed. Serre correctly used "dans" and did not us the symbol .
  • section 7, pg. 22, in proof of Prop. 21, 2nd paragraph, 3rd sentence, replace "contain" with "contains".
    • 4th sentence: should be, "... we must have " not . [separable consequence is later, namely in the Corollary(!)]

Chapter 2

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  • sec 1, pg. 28: third sentence should be "one sees that E is the union of (A:xA) cosets of modules xE,...". As is in the book, the sentence does not make grammatical sense.
  • sec 2, pg. 29: the def. of w must carry a v' not just v, that is: w = (1/m) v' is a discrete valuation of L.
  • sec 3, theorem 1, (i): change K to ; so the completion of has degree over the completion of K.
  • sec 3, exercise 1: the suggested reference should say Section 3 of Bourbaki Algebra, not 7. (going by Hermann Paris 1958 as usual)

Chapter 4

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  • sec 1, pg. 63, prop 3, need K' (not K) in def. of e', that is: .
  • in the proof of prop 3, the s and t for "st, t in H" need to be italicized.
  • sec 2, prop 6, first line of proof: gothic beta should be gothic p, that is to each x in
  • sec 3, lemma 3, last line of proof: upper case Phi is nowhere defined, need lower case phi, that is: phi'(u)....so theta and phi must coincide.
  • sec 3, statement of lemma 5, again phi, not Phi.

Chapter 6

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  • sec 3, at the top of page 102, should be " ... = (\psi,a_G)_H = ... = \lambda(\psi,r_H)_H + f_{K'/K}(\psi,a_H)_H = ...

Chapter 5

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  • sec 7, lemma 9, replace with

Chapter 7

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  • sec 1, in the definition of induced module, replace the second occurrence of with

Chapter 8

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  • sec 5, prop 9, replace with

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Notability

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  • Okay, citing the article Wikipedia:Notability (books), Serre's Local Fields qualifies as notable under articles (1) and (5) in the nutshell box. From its citation count in MR I cite article (1), and from the (mathematical) historical significance of Jean-Pierre Serre, I cite (5). I added a bibliographic reference to the book, which includes its reference number for MR, where one can have a look at its citation count. —Preceding unsigned comment added by 69.181.233.136 (talk) 05:37, 10 April 2009 (UTC)[reply]
  • Henrytucker, notability is much more losely defined than most editors would like to admit... anyway, check the link provided by 69.181.233.136 above; adding some good references should do the trick. Note that I do not think this is non-notable, just that it lacked any source supporting it - probably a {{refimprove}} tag would be better than {{notability}}... my bad. And yes, we could use more and better such articles, on the books themselves and alos using those pioneering books as references in the articles about their subjects (that's a way to help readers find the books, and actually one of the best things about WP: a place to find good start up information and good references to read and get indepth info if you want to). 69.181.233.136 makes a good point that item (5) on the cited list is probably enough. Still it would be nice to have references that do not require any special access rights. - Nabla (talk) 15:16, 10 April 2009 (UTC)[reply]