Talk:Iwasawa theory

message: I have made some minor changes in the history page. 
I have put the sentences about Euler System methods in a separate paragraph before the announcement of Skinner-Urban, since it was ten years prior.
I have also removed the reference to Urban-Skinner's "note aux CRAS" which was a mistake, since this note has nothing to do with the main conjecture (it is a different announcement by the same guys). 
In my opinion, the whole Urban-Skinner paragraph could as well be suppressed, since it does not 
meet  Wikipedia's "verifiable source' requirement.  —Preceding unsigned comment added by 160.39.47.33 (talk) 11:11, August 28, 2007 (UTC) 
:Does anyone knows if Skinner's and Urban's proof is valid or not? --85.76.80.222 (talk) 16:59, 9 December 2014 (UTC)
thread_title:  Urban-Skinner 

message: Ive always thought that the comment that "Iwasawas originality was to go off to infinity in a new direction" was completely without mathematical content, and not even useful as a vague explanation of what iwasawa theory is.  In case anyone out there likes it, I wanted to leave a note to let you know that I was erasing it and give you a chance to change it back.
Jrdodge (talk) 03:49, 8 September 2009 (UTC)
replies: text: Well, sorry about that. There is a general issue with heuristic remarks: they may have content that is not "mathematical content". As we know, mathematics can exist fine without any commentary at all. But do you really think that mathematics articles should only have such "mathematical content"? Over time (I mean five or six years) I have seen many people purge such remarks from Wikipedia. They tend not to add better heuristics of their own. In other words these edits tend to be purely negative. I wonder who else besides (pure) mathematicians think that no explanation at all its better than some vague explanation. It is not the kind of feedback we usually get, certainly. Charles Matthews (talk) 05:25, 8 September 2009 (UTC)
replies: text: I think the comment about the new direction is a useful one. Perhaps it would help to find a source to support the claim. One certainly uses this kind of language in the field, speaking of the cyclotomic direction, the anticyclotomic direction, etc. I'll see if I come across something in the literature that makes such a claim about Iwasawa's originality. RobHar (talk) 08:47, 8 September 2009 (UTC)
replies: text: The article could do with a whole section on the context. The remark was an old one: the Springer EoM link has some general comments about the analogy between finite field extensions and adding more roots of unity. There is probably something about the heuristics in Coates, J.: K-theory and Iwasawa's analogue of the Jacobian. In Algebraic K-theory II, p. 502-520. Lecture Notes in Mathematics 342. And other early papers of John Coates who (I guess) coined the term Iwasawa theory; certainly "main conjecture". There seem to have been many papers linking the main conjecture to the Bloch-Kato conjecture on Tamagawa numbers. I'm a bit out of touch, but I guess that that conjecture is not (equivalent to) the Bloch-Kato conjecture in K-theory that was announced completely proved earlier in the year. In other words, there is some pre-context and post-context to supply. Of course general expansion is required, also. Charles Matthews (talk) 18:22, 8 September 2009 (UTC)
thread_title:  Iwasawa's originality 

message: I'm not a number theorist, so I might be missing some notation convention, but isn't it meant to be Z/p^nZ, not Z/p^n in the formulation paragraph?
:Z/pn is another notation for Z/pnZ. Z/(pn) would be more proper, but I've certainly seen it both ways. RobHar (talk) 18:18, 12 August 2010 (UTC)
replies: text: It looks like a series of edits over the years turned this example into a false one. I've fixed it. Thanks. RobHar (talk) 22:12, 11 October 2010 (UTC)
thread_title:  Formulation