Talk:Complex multiplication

message: I am expecting multiplication in the complex field at this(Complex multiplication) title. --MarSch 12:52, 3 Jun 2005 (UTC)
replies: text: How's that? Dmharvey Talk 16:57, 3 Jun 2005 (UTC)
replies: text: better than nothing --MarSch 18:31, 3 Jun 2005 (UTC)

text: I'm attempting to figure that out right now... I have a very good understanding of undergraduate mathematics, and a beginning understanding of set theory, group theory, analysis, et cetera. I'm finding this article somewhat difficult to follow, but I really, really want to know the answer to the question you asked, so I'm going to try. --Monguin61 04:12, 15 December 2005 (UTC)
replies: text: If "undergraduate mathematics" does not include at least "set theory, group theory, analysis, et cetera", I'm a bit curious what it does include... Michael Lee Baker (talk) 04:39, 29 July 2015 (UTC)

message: I guess this is evident to anyone who knows what theyre doing, so maybe the article doesn't need the notation explained, but I was wondering if anyone could tell me what 
: \mathbf{Z}\left[ \frac{1+\sqrt{-163}}{2}\right]
actually means? I assume the Z denotes a group of some sort, and the stuff inside the brackets is a parameter defining the group, but what type of group exactly? Or am I totally off? --Monguin61 04:24, 15 December 2005 (UTC)
replies: text: Z[α] is the subring of the complex numbers generated by the complex number α if you want it in simple terms. Charles Matthews 08:53, 15 December 2005 (UTC)

text: I will add a link explaining this notation. But I cannot either follow the "explanation", I mean, some more details (even if unprecise and handwaving), or at least an "external link" seem necessary, because readers come from "far away" to this page (referred to in pi and other places), hungry for this explanation (why dist( exp(...), Z) is so small )). — MFH:Talk 14:14, 16 March 2006 (UTC)
thread_title:  Trying to follow explanation 

message: The equation α²=α-81 should be α²=α-41 on this page  —Preceding unsigned comment added by 192.91.173.36 (talk) 01:47, 7 February 2010 (UTC)
thread_title:  correction 

message: To reduce confusion, the name of this article should be changed. I suggest it be changed to either "Complex multiplication (elliptic curves)" or "Complex multiplication (elliptic functions)" Wideangle (talk) 00:22, 31 March 2010 (UTC)
replies: text: No, there is no requirement to disambiguate in that fashion: adding things in parentheses, except where there is another article of a related name, is against general title conventions. Charles Matthews (talk) 14:06, 31 March 2010 (UTC)
replies: text: I'm not saying that there is a requirement to make such a change. I am suggesting that the change be made in order to reduce confusion. The vast majority of people who think they know what "complex multiplication" is think that it means the multiplication of complex numbers (which makes a lot of sense, by the way). My background is: BA in Mathematics from the University of California at Berkeley. And yet, I never encountered the "elliptic curves" meaning of "complex multiplication" until three days ago when I came upon a link to this article in the John Tate article. Wideangle (talk) 00:52, 3 April 2010 (UTC)
replies: text: There is a hatnote explaining that the article is not about multiplication of complex numbers. Looking at Wikipedia:Article titles, the title seems to conform to the points Recognizable (commonly used in reliable sources), Easy to find (names and terms that readers are most likely to look for in order to find the article), Precise, and Concise. Basically there is nothing in that guideline to justify a change. Charles Matthews (talk) 08:39, 3 April 2010 (UTC)
replies: text: Regardless of what the article's title is, I think this point should be made clearer -- It's surprising easy to overlook the note (I did), and I think a good many readers will be expecting information about multiplying complex numbers. KLuwak (talk) 15:49, 28 February 2011 (UTC)
thread_title:  Article's name should be changed 

message: The first section of the article is quite rough and could benefit from a rewrite ("ring of analytic automorphic group" doesn't make any sense; "ring of automorphisms" should read "group of automorphisms"; \mathbf{C}^3 is incorrectly used when we should be speaking of the projective plane; grammar is generally poor and so on). I may eventually get around to it. Michael Lee Baker (talk) 04:33, 29 July 2015 (UTC)
thread_title:  First section of article 

message: In fact, a definition of its subject is the only thing that every encyclopedia article must have. Yet this article lacks such a definition.
(The article does say the following:
"Consider an imaginary quadratic field K=\mathbb{Q}(\sqrt{-d})\ , d \in \mathbb{Z}, d>0.
An elliptic function f is said to have complex multiplication if there is an algebraic relation between f(z) and f(\lambda z) for all \lambda in K ."
The concept of an "algebraic relation" between two functions f(z) and g(z) would normally mean that there is a polynomial P(X,Y) in two variables such that for all values of z that make sense, we have P(f(z), g(z))  =  0.
But in this article we are not told whether the coefficients of P(X,Y) are merely complex numbers, or if they are required to belong to the field K.
Or am I missing something?2600:1700:E1C0:F340:ED3B:6DA2:E8FC:C260 (talk) 00:22, 24 May 2019 (UTC)
thread_title:  Article needs a definition of its subject 

message: I don't understand why an elliptic curve over a finite field has an endomorphism ring larger than the integers, due to the Frobenius endomorphism. What is it I do not understand? The Frobenius endomorphism is an endomorphism on a comnutative ring with characteristic p. Hence the refered Frobenius endomorphism cannot be an endomorphism on the elliptic curve itself. But if it has to be an endomorphism on the ring of endomorphisms - what makes sense, but this ring is not abelian in general. If the field is a prime field with charateristic p, a point on the curve has coordinates x and y, and the Frobenius endomorphism, defined for the elliptic curve, maps x -> x^p=x, and y -> y^p=y, hence it is the identity. Madyno (talk) 22:21, 13 December 2021 (UTC)
thread_title:  Finite field 

message: From ghe introduction: CM means the ring of endomorphism is larger than \Z. This may raise the idea the ring should contain the integral numbers or should be infinite. In my opinion the correct formulation would be there is a non-trivial endomorphism, that is an endomorphism not induced by the integers. Madyno (talk) 23:15, 7 December 2021 (UTC)
thread_title: Intro