Talk:Local Fields

First talk

• I'm a student of Robert F. Coleman at U.C. Berkeley and we decided to add an article on Serre's famous Corps Locaux because it is (a) a seminal work in the field, and (b) we felt that the errata needed a public place to be hosted. For other books in our category, cf. Robin Hartshorne's Algebraic Geometry (book). Henrytucker (talk) 07:42, 12 March 2009 (UTC)

Errata

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)

/*copy from article's 'errata' START*/

Errata

Chapter 1

• section 4, pg. 14, 2nd centered display: the ramification indices should be $e_{\beta }$ not $e_{p}$ in the product.

• section 5, pg. 15, first formula needs to be $N:I_{B}\rightarrow I_{A}$, Not the other way around.

• section 6, pg. 17, last sentence of first paragraph, replace the inclusion symbol $\in$ 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 $\in$.

• section 7, pg. 22, in proof of Prop. 21, 2nd paragraph, 3rd sentence, replace "contain" with "contains".
  • 4th sentence: should be, "... we must have ${\bar {L}}_{S}={\bar {K}}_{T}$" not ${\bar {L}}$. [separable consequence is later, namely in the Corollary(!)]

Chapter 2

• 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 ${\hat {K}}$; so the completion of $L_{i}$ has degree $n_{i}$ 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

• sec 1, pg. 63, prop 3, need K' (not K) in def. of e', that is: $e'=e_{L/K'}$.

• 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 $p_{L}^{i}$

• 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

• 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

• sec 7, lemma 9, replace $\sum _{i=0}^{i=r-1}$ with $t+\sum _{i=1}^{i=r-1}$

Chapter 7

• sec 1, in the definition of induced module, replace the second occurrence of $A$ with $\Lambda$

Chapter 8

• sec 5, prop 9, replace $A_{Q}$ with $A_{G}$

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Notability

• If an article on Serre's Local Fields is not "notable," then let me recommend deleting Robin Hartshorne's Algebraic Geometry and Saunders Mac Lane's Categories for the Working Mathematician. Alternatively, a more productive endeavor would be to produce articles on more mathematics texts, with a good starting point being Springer's GTM. Henrytucker (talk) 05:19, 7 April 2009 (UTC)

• Hi! It may be notable - I do believe it is - but... how do we know? Cite some source, please. - Nabla (talk) 11:11, 7 April 2009 (UTC)

• What kind of source can qualify "notability"? If you have access to MathSciNet, then check its citation count in Mathematical Reviews, which is 346 (ref. MR0554237). That's fairly notable. I also have correspondence with both Mike Zieve and Robert Coleman citing the book as the canonical exposition of higher ramification groups. And finally, as a mathematician, I can assure that the vast majority of my field would cite the entire Springer-Verlag GTM series as being "notable," as I've said before. Other books in the series that are standard-setting include the already mentioned Algebraic Geometry and Categories for the Working Mathematician, as well as Serge Lang's Algebra, Paul Halmos's Measure Theory, Zariski & Samuel's Commutative Algebra, and John L. Kelley's General Topology. Wikipedia definitely has room for articles on the majority of the GTM, and it would be appreciated by your average individual searching for information on where to go for certain topics in math. Henrytucker (talk) 08:35, 9 April 2009 (UTC)
• Also, I notice the notability of neither Mac Lane's nor Hartshorne's books has been brought into question where they also seem to lack any sort of reference otherwise. Henrytucker (talk) 08:41, 9 April 2009 (UTC)

• 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)

• 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)