Cassels and Fröhlich. First printed in , this book has been essential reading for aspiring algebraic number theorists for more than. Solutions to the Cassels-Fröhlich exercises. Dorian Ni. May First of all, many thanks to Kevin Buzzard for his kind help, and for his willingness to answer . Cassels–Froehlich errata. July 18, Consider what God has done: Who can straighten what he has made crooked? Ecclesiastes 1 These errata.
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I can only assume the LMS is now selling it but have no details. Ok, the deadline has past, I’ve fohlich days going through the results, and I have collated them all here: I will update this file as comments come in. The London Mathematical Society would like to know all the errors I’ve made myself, by 12th of February, so feel free to let me know of anything, however trivial! I clearly misjudged thisthe question has a good few upvotes now. Hence the LMS had to go about contacting the authors of the original articles.
When they contacted Serre he replied “sure reprint my articles, but please include the erratum that I indicated in my completed works. I looked over the thread casels last October about the errata database but the database doesn’t seem to contain this book.
On the other hand it is surely a very widely-read book. I think I just found a typo in the definition of a co-induced module on p The notation is also terrible: Does anyone else have any scrawled marginal notes in their copies of Cassels-Froehlich about typos or other things that the LMS can fix? They are planning on having an erratum page at the beginning of the book when they reprint it.
Introduction to Algebraic Number Theory
Discussion on this thread is happening here at the meta. After this point I KB will put all the errata we have caught into one file and the LMS will send it to the authors, asking for their approval.
Anton and Ilya have suggested that really this would be better if it had one big answer rather than lots of smaller ones. But let me persist with the “lots of smaller ones” for the time being, because I am still getting emails with non-trivial lists in from different sources and, although I want to put everything together into one pdf file, I don’t really want to do it until I am pretty sure no more is coming in.
On the other hand these partial lists have definitely been of help to some people, ccassels. I’ve had emails saying “I have a big list of corrections; here are the ones that haven’t already been mentioned. OK, so all the people whom I was almost sure would have comments have now got back to me.
I posted everything in one “burst” so as to only bump this post to the top one last time. What I frholich do now is to compile everything I have now on the basis that I am not expecting much more into one pdf list, and post a link to it.
Ok so it looks like I misjudged this and the community seem happy to have the question here, at least casseps present. After “can be taken to be rational integers” add the following parenthesis: And here’s one which I spotted: I think that the last full sentence at the bottom of p98 is wrong. I think the “action” they define is not an action, and I think the first couple of sentences of section 4 should be:. I posted this question in several other places as well the nmbrthry mailing list, and sci.
Here, completely unedited, is the bulk of an email I just got from Rene Schoof. Schoof’s list will be very useful; its length shows that the new edition will cassesl at least one or two pages of corrections. It should be d f. In my copy of the book, the footnote does not refer to Stalin.
The only mention of that name is on p. This is a delicate one. This answer is just to bump this post up to the front page for the final time. I typed up all the errata I heard into dassels pdf file and put it here. Keith Conrad sent me a nice chunky list here. Here’s one I didn’t see on the list on mathoverflow: The right-hand side should be the reciprocal of what it is in the book. I recall also having trouble getting the signs in part 14 of that exercise on cubic reciprocity to work out, perhaps because of the mess of algebra, perhaps because some of the computations depend on part Below my 51 errata that I didn’t see on your list or in William Stein’s mail yet.
Most are of a typographical nature, but some have mathematical substance.
books – Erratum for Cassels-Froehlich – MathOverflow
I did at the present occasion not verify the correctness of those. I did not do any proofreading of my casse,s either!! I trust you will apply your own sound judgment. Page 3, Proposition 1. This Proposition is misstated, and the proof has the wrong reference: The Theorem in the latter section is the correct formulation: More or less coincidentally, the Proposition is correct as stated exercise!
Page 98, the lower “delta” in the diagram should have a “hat” the upper one has one, though it is barely visible in my copy. Pageline 3 of section 2. Pageline Also, the proof is confused. Pageline counting the footnote as This is what I scrawled, I did not verify it at the present occasion!
Should be indexed by U in the limit process, not UH. Also, the verification that the displayed map is actually inverse to the Artin map seems to merit a tiny bit of explanation using the identification of artin map with cup product against fundamental class in Serre’s treatment of the local case.
Q]and the definitions of f and g should subtracting some stuff. The Brauer argument below makes frrohlich all moot.
Thanks to everyone that contributed. Why is this borderline? This actually seems to me an ideal frohlicy of the collected attention of Math Overflow to do something that helps the community more generally.
I agree, this seems froblich an excellent question. And I’m glad to hear that Cassels and Froelich may be reprinted! It’s “borderline when it comes to what I want MO to be” ;- which is just loads of fun precisely-worded questions with precise answers. But judging by the upvotes I have misjudged this. I also emailed some people asking them if they had seen any typos.
I’ll post anything I get. In my opinion this is an excellent example of a good community wiki question! If you think the typos really are typos, vote up: I think the “action” they define is not an action, and I think the first couple casseks sentences of section 4 should be: Z should be bold face.
No correction is needed: I do not understand what change Schoof wants. The letter Z in Z[zeta] should be in boldface. Bill Stein independently got in touch with me to tell me about the two typos on p99 he’s giving a talk on that chapter in 30 minutes’ time!
I trohlich Serre explaining long ago that the reference to Stalin was a fronlich joke linked to NATO’s sponsorship of the conference.
I think this is a typo? Actually, I think the entire proof of Prop. I may have made an error, but I think page isn’t actually mistaken: Oesterle points out that the “standard” definition of a co-induced module is Hom Lambda,X with G-action g.
If this definition is used then what the authors write seems to be OK. However it seems to me that implicit in the article is a “non-standard” but isomorphic to the standard definition.
I happened to notice these misprints this morning: I’ve started reading chapter 1. Could someone confirm that the following are typos? Page 45, line 5: Page 52, part 3 of the first definition: Page 54, line Page 73, line 6: Page 75, line 1: