## “Le Groupe Fondamental de la Droite Projective Moins Trois Points” is now online

The three papers that influenced me the most at the beginning of my mathematical career were “Rational Isogenies of Prime Degree,” by my advisor, Barry Mazur; Serre’s “Sur les représentations modulaires de degré 2 de $\text {Gal}({\overline {\Bbb Q}}/{\Bbb Q})$;” and Deligne’s 200-page monograph on the fundamental group of the projective line minus three points.  The year after I got my Ph.D. I used to carry around a battered Xerox of this paper wherever I went, together with a notebook in which I recorded my confusions, questions, and insights about what I was reading.  This was the paper where I learned what a motive was, or at least some of the things a motive should be; where I first encountered the idea of a Tannakian category; where I first learned the definition of a Hodge structure, and what was meant by “periods.” Most importantly, I learned Deligne’s philosophy about the fundamental group:  that the grand questions proposed by Grothendieck in the “Esquisse d’un Programme” regarding the action of Gal(Q) on the etale fundamental group $\pi := \pi_1^{et}(\mathbf{P}^1/\overline{\mathbf{Q}} - 0,1,\infty)$ were simply beyond our current reach, but that the nilpotent completion of $\pi$ — which seems like only a tiny, tentative step into the non-abelian world! — nonetheless contains a huge amount of arithmetic information.  My favorite contemporary manifestation of this philosophy is Minhyong Kim’s remarkable work on non-abelian Chabauty.

Anyway:  Deligne’s article appears in the MSRI volume Galois Groups over Q, which is long out of print; I bought a copy at MSRI in 1999 and I don’t know anyone who’s gotten their hands on one since.  Kirsten Wickelgren, a young master of the nilpotent fundamental group, asked me the obvious-in-retrospect question of whether it was possible to get Deligne’s article back in print.  I talked to MSRI about this and it turns out that, since Springer owns the copyright, the book can’t be reprinted; but Deligne himself is allowed to make a scan of the article available on his personal web page.  Deligne graciously agreed:  and now, here it is, a publicly available .pdf scan of “Le Groupe Fondamental de la Droite Projective Moins Trois Points.”

Enjoy!

## 12 thoughts on ““Le Groupe Fondamental de la Droite Projective Moins Trois Points” is now online”

1. Dear Jordan,

I don’t know why we haven’t discussed this before (or perhaps we have and I’ve just forgotten). In any case, we seem to be of very similar minds: the two papers I regarded as “desert island” material when I was beginning my career were Mazur’s paper on the Eisenstein ideal, and this paper of Deligne. Each of them contains an incredible amount of arithmetic and geometry.

Best wishes,

Matt

2. Jay says:

Hot.

3. Ken Ribet says:

I was perplexed by the passage “since Springer owns the copyright, the book can’t be reprinted.” Springer has every reason to want to keep the book in print! I’ve alerted them to the list http://www.msri.org/communications/books/masterlist.html . If we’re lucky, these books will appear on http://www.springerlink.com/ as well as on Amazon. I’d certainly like to have the “Galois groups over Q” volume available!

In principle, there should no longer be such a thing as an out-of-print book. The “print on demand” technology has gotten to the point where it is worth a publisher’s while to print a very small number of copies of a back title for which there is still demand.

4. JSE says:

Ken: Perhaps I should expand that to “since Springer owns the copyright and doesn’t want to reprint it.” I have no idea why Springer doesn’t think it’s worth their while to reprint the book; do you?

Matt: Believe it or not, as soon as I put up this post I thought, “Matt’s going to comment that he was reading the Eisenstein ideal paper, not the rational isogenies paper…!”

5. Ken Ribet says:

Who in Springer was consulted, and what did they say? It simply doesn’t make any sense to me that they would refuse to reprint a book for which there is demand, especially if the book is part of a series.

6. I agree with Ken that it seems odd that Springer doesn’t want to reprint it — they’ve gone to using a glorified laser printer to produce very small runs of their older books, which is why the quality of such is annoyingly poor…

7. Anonymous says:

I must have looked explicitly for that book in second hand bookstores at least 20 times (without success, obviously). If only an extra copy of this book had been printed for every 20 copies of “rigid local systems”… (not to disparage the latter, but why does _every_ second hand book store in america have a book by Katz in their math section?)

8. Philip Horowiitz says:

I don’t know about the reprinting but it is usually fairly easy to find a second hand copy on the net for a price which is not too outrageous. There is one currently listed on amazon.com at $170 which is presumably not significantly more than Springer would charge if they ever do get round to reissuing the book 9. David says: Amazon now claims to be selling new copies “Galois groups over Q” – no “out of print” warnings or anything – at$64.95, so I ordered a copy. We’ll see what happens.

10. george s says:

what happened, david? i’ve been waiting five years for you to reply, checking this site several times a day, and finally my patience is up. tell me.

11. K says:

Is there an English translation?

12. JSE says:

Not that I know of! But my French is terrible and it wasn’t too hard for me to read.