Talk:Weil conjectures

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[edit] Move

I moved the page here because it is a group of conjectures. LittleDan 17:26 12 Jun 2003 (UTC)

I think the conjectures was made mainly by taniyama. you should mention the fact it is now calld shimura-taniyama conjectures. http://www.fact-index.com/t/ta/taniyama_shimura_theorem.html

No, you are mistaken about that. These Weil conjectures were made by Weil around 1949. The Taniyama-Shimura conjecture was made about the time of the conference in Nikko, in 1954.

Charles Matthews 16:29, 20 Sep 2004 (UTC)

[edit] Who?

Who proved these? Deligne? Others? Many others? Deligne seems to have gotten a Fields medal for this or at least something related.

Dwork and Deligne are responsible for the proofs themselves, Weil gets credit for the conjectures, and Grothendieck is responsible for creating the theory of etale cohomology which was used by Deligne in his proofs. - Gauge 20:45, 10 July 2005 (UTC)

Some credit goes also to Mike Artin, I think. Charles Matthews 21:16, 10 July 2005 (UTC)

Per Allyn Jackson's article [1] on page 1203, it lists B. Dwork's solution of part 1 as being from 1959 (versus 1960 in the article text), and it lists A. Grothendieck as the solver of part 2. It also mentions Grothendieck as having provided a more general solution to part 1 in 1964. Myasuda 14:24, 9 September 2006 (UTC)

[edit] finite fields or algebraically closed fields of prime characteristic?

My knowledge of algebraic geometry is tiny, but it is usu. done over algebraically closed thus infinite fields, isn't it? So I wonder if the current 1st sentence with "...algebraic varieties over finite fields." might be incorrect. Rich 15:43, 23 August 2006 (UTC)

I've added a para of further explanation. Charles Matthews 08:35, 24 August 2006 (UTC)