# A reference and an explanation needed?

In my previous question I was asking for a method to construct a global point if we have local points with us which is here, but I got an answer, it didn't serve the entire purpose, but later on due to my struggle in finding the answer I have find the following statement while I was leafing through internet.

The statement was :

In a highly influential 2001 paper, Henri Darmon proposed a systematic, conjectural "modular" construction of algebraic points on elliptic curves. Using p-adic analysis, he constructed local points on elliptic curves, conjectured them to be global points, and gave precise predictions governing their field of definition. This construction is genuinely novel in that it lies outside the scope of the theory of complex multiplication.

So I was left only with that statement, can anyone take initiative in giving the exact article which the statement was referring to.
And I would be still happy if some noble person gives an outline of the procedure or a brief overview.

Thanks a lot. cordially, Iyengar.

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The statement the OP refers to is from here: birs.ca/events/2011/5-day-workshops/11w5125 ("Objectives" section). – Srivatsan Nov 15 '11 at 5:46
Thats right sir, I was unable to find the exact paper @Srivatsan – Iyengar Nov 15 '11 at 5:54
But sir why didn't everyone forsaken me? , is there any problem in my formatting or with my actions? @Srivatsan – Iyengar Nov 16 '11 at 14:01
I cannot speak for anyone else, @iyengar. I do not understand this area well enough to contribute meaningfully. That said, generally speaking, I do not think that you put enough effort into constructing your question. Your language/punctuation seems much better in this post (keep it up!), but I am not impressed with the content. Picking a random statement from the internet (without acknowledging the source) and asking to elaborate it does not make a good question IMO. – Srivatsan Nov 16 '11 at 14:41
But to add something, if I had known the source of this statement why is there a need to ask the question sir? , I might have studied myself, that statement was exactly sent to me by an editor of journal, and its by you I learnt that simply copy-pasting of the statement in google could give the link, but I was successful upto then but later on failed to find an exact paper ! @Srivatsan – Iyengar Nov 16 '11 at 14:55

If you looked in google scholar for author:h-darmon you would find that there is only one paper in 2001 with big number of citations. (Note that you can easily search in google scholar - you can choose which scientific disciplines you want to search, you can specify author and even range for the years. Google also tries to find papers citing given paper and papers which are related to the given paper - which is more difficult to automatize, so here you can sometimes find weird results. Just click on Advanced Scholar Search to see many search options you have there.)

• H. Darmon Integration on $\mathcal H_p \times \mathcal H$ and Arithmetic Applications. The Annals of Mathematics, Second Series, Vol. 154, No. 3 (Nov., 2001), pp. 589-639. Link at jstor, author's page.

If you had closer look at http://www.birs.ca/events/2011/5-day-workshops/11w5125 from which you have that quote you could find this, where the same paper is mentioned. If you did not want to browse the whole site of the workshop, you could have tired to google for darmon site:www.birs.ca 2001. BTW including the link to the webpage from which you have the statement would make it much easier for us to help you track down the paper.

You might also find useful to have a look at answers to this question: Finding a paper