Talk:Absolute Galois group

Untitled

Would I be right in thinking that a projective profinite group is a projective object in the category of profinite groups? I've just been looking at a definition (John Stuart Wilson, Profinite groups, p. 75) and this looks about right, but I could be missing something. Charles Matthews (talk) 21:39, 26 November 2009 (UTC)[reply]

Someone (Barylior) wrote that the absolute galois group of a p-adic field is known by generators and relations, but it does not seem to be the case up to my knowledge (see also Abrashkin's note OW06.ps about the current status of things, dated 2006). Am i missing anything? Myrizio (talk) 11:47, 19 December 2009 (UTC)[reply]

Would be surprising, really? The unramified part, yes. But this article does need updating. Charles Matthews (talk) 14:40, 19 December 2009 (UTC)[reply]

It would not be totally surprising, and yes the unramified (or even the tamely ramified) part are known with generators and relations, but they are not the "absolute galois group", so a citation (and possibly a correction if the full absolute group is not known) is required. 192.167.204.254 (talk) 14:59, 19 December 2009 (UTC)[reply]

High Importance

Why is the article of hight importance?KlappCK (talk) 15:14, 15 September 2011 (UTC)[reply]

Well, it's a pretty fundamental object to study. Understanding the absolute Galois group of the rationals is ostensibly the purpose of algebraic number theory. I think this topic fits well in the list of other topics that are high priority in number theory. RobHar (talk) 17:11, 15 September 2011 (UTC)[reply]

Assessment comment

The comment(s) below were originally left at Talk:Absolute Galois group/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Arguably top importance (the absolute Galois group of the rationals!), and somewhat understated. Geometry guy 00:36, 22 May 2007 (UTC)[reply]

Last edited at 00:36, 22 May 2007 (UTC). Substituted at 01:43, 5 May 2016 (UTC)

Dives too fast into inpenetrable jargon

Given how wonderful and important the Absolute Galois Group of the Rationals is, should this encyclopedia try to explain it to intelligent, but semi-technical people, with decent school level mathematics>? I understand what roots of equations are, and I understand what a Group is, and what a Galois Group is for that matter. I am curious about this mysterious Absolute Galois Group (having read about it elsewhere). This article is, in that respect, hopeless. It fails to help me, and I have a physics degree (or two). I cannot see who this article is for, except for professional mathematicians. Should not mathematicians not desire to explain this jewel to the layman? I'm not saying to dumb down the existing content, but rather to build up to it with some human explanation.