Sep 182013

Steve pointed out the thing that makes EGA difficult to read is not that it is dense, but rather that it is gigantic.

Robin Hartshorne’s book algebraic geometry is an edulcorated version of Grothendieck and Dieudonné’s EGA, which changed algebraic geometry forever.

EGA was so notoriously difficult that essentially nobody outside of Grothendieck’s first circle(roughly those who attended his seminars) could (or wanted to) understand it, not even luminaries like Weil or Néron .

Things began to change with the appearance of Mumford’s mimeographed notes in the 1960’s, the celebrated Red Book, which allowed the man in the street(well, at least the streets near Harvard) to be introduced to scheme theory.

Then, in 1977, Hartshorne’s revolutionary textbook  algebraic geometry was published. With it one could really study scheme theory systematically, in a splendid textbook, chock-full of pictures, motivation, exercises and technical tools like sheaves and their cohomology.

However the book remains quite difficult and is not suitable for a first contact with algebraic geometry: its Chapter I is a sort of reminder of the classical vision but you should first acquaint yourself with that material in another book.

GTM 52 的精华是第 2, 3章, 分别介绍 Scheme 和它上面的 Cohomollogy theory.

GTM 52 有习题 464 道. 这本书的习题, 非常重要! 当然, 习题也不一定必须一个一个全部做完.

Oct 012012

北京大学数学科学学院的周健老师正在把 EGA 与 SGA 翻译成中文. 早在 \(05\) 年(也可能是 \(06\) 年, 记不清了), 我就听说他在进行这个工作. 嗯, 这是艰难的事业.

依照丘成桐先生的建议, 为方便广大青少年学习者, 设立EGA, SGA. 这里包括了 EGA 与 SGA 的中文译本, Bourbaki 的数学原理 看样子也会加进来. EGA 的相关资料也会收集整理, R. Godement, J.-P. Serre, P. Deligne, M. Raynaud 的几篇文章已经呈现在读者面前, Ngô Bảo Châu(吴宝珠)证明基本引理(fundamental lemma for automorphic forms)的文章也已经翻译完成.

翻译文档会即时更新在这里, 请仅仅使用在个人学习的用途上.