# Serre's FAC in English

Has somebody translated J.-P. Serre's "Faisceaux algébriques cohérents" into English? At least part of it?

In a fit of enthusiasm, I started translating it and started TeXing. But after section 8, I got tired and stopped.

However if somebody else already took the trouble, I would be most grateful. I do not know a word of French(except maybe faisceau), and forgot whatever I learned in the process of translation very quickly.

This is made community wiki, as I do not want to get into rep issues. Please feel free to close this if you think this qn is inappropriate for MO(I have added my own vote for closing, in case this helps). I would be happy to receive answers in comments.

• At the risk of getting booed, I would suggest just reading it in French. After all, it won't be the last time you'll need to read something published in French, and in my opinion translating things to English is probably less productive than just trying to read them and thinking about the words. I left the U.S. for France after my undergraduate years, never having studied or spoken French in my life before that, and I was able to get up to speed reasonably quickly by doing this. Besides, if you want to follow any of the references, you'll have to translate those too ! – xuros May 4 '10 at 9:12
• No booing at all -- if a paper as fantastic as GAGA doesn't provide enough inspiration to learn basic math French (which is really not hard; I can't read a French menu and have read thousands of pages of math French), then what will such a person do when confronted with a less dramatic paper which has to be read? Serre has written books in English and French. Compare them side by side, make a list, practice, learn to read. It's easier than the math! – BCnrd May 6 '10 at 1:49
• I won't boo, but my view is that the more translations the better. Someone whose field has virtually no papers in French but wants to cite something from FAC may want to look at the original without having to learn French. mathoverflow.net/questions/43147/… Some people may have more trouble than average learning foreign languages. And the existence of a translation does not prevent anyone from ignoring it and struggling with the French original if they want. How can it be bad to provide the math community with more options? – Timothy Chow Oct 25 '10 at 14:22
• Some of the comments on a similar type of MO question mathoverflow.net/questions/33348/theorem-of-borel-and-tits are relevant here, I think. Translations are convenient when they exist and are well done, but lots of important French mathematics won't get translated. – Jim Humphreys Oct 25 '10 at 16:26

Together with some help from my friend, I translated FAC into English. I didn't have so much time to proofread it, so probably there are some mistakes.

It can be found here: FAC, Source.

• Very impressive. This is a great contribution from you to all students of algebraic geometry. Thank you very much. Bless your kind soul! Wish you all the best. – Anweshi Oct 26 '10 at 18:06
• Just started reading your translation. Thanks! Page 9, the paragraph above Proposition 1, I believe you want $t \in \mathscr{F}_U$. – Prince M May 10 '18 at 6:44
• Proposition 2 page 25 is missing a " ' " – Prince M Dec 17 '18 at 22:05
• Proposition 3 page 26 there is a subscript "j" that appears twice that should presumable be an "h" – Prince M Jan 8 '19 at 23:43
• page 27 n23, $(\phi \circ \psi)^{*}$ is missing its equality – Prince M Jan 21 '19 at 23:59

This is not an answer to your question, but I can't resist, especially with community wiki, pointing you to a (in my novice opinion) good translation of GAGA here by my former office mate Trevor. He probably knows if there is a FAC translation, but he is not on MO. You can try to email him.

• Oh GAGA translation already exists! Sir, if we were talking in real life, I would have jumped on you and hugged you! Thanks a lot! :) Sorry I can't upvote you now, in an urge for earning the "Civic Duty" badge, I spent all my votes for today... :( – Anweshi Feb 6 '10 at 17:51
• @Anweshi: No problem! – Hailong Dao Feb 6 '10 at 17:55
• Damn/Woohoo! I was halfway through my own GAGA translation. – Sean Rostami Feb 19 '10 at 0:54

There is another translation by Andy McLennan that comes with a lot of background material, the actual translation starts at page 235. I'm not really competent to make any comparisons.

• Broken link ... – ArB Oct 18 '20 at 7:36
• @ArB Thank you. It should work now. – Michael Greinecker Oct 19 '20 at 8:07